Dracaenas are sensitive to both Chlorine & Fluoride in tap water. That's most likely the reason for the tips of the leaves turning brown like that. You can try leaving some water sitting out for at least a day, giving the Chlorine time to evaporate away. I don't think that there's much you can do about the Fluoride tho, it can't evaporate. Leaving the tap water sitting out for at least a day might work. For some people it does, but others it doesn't. I tried this method out when I bought a couple of Dracaenas. It seemed to work fine at first, then one of them started showing signs of browning too, but only on a couple of leaves. Luckily, I was closely monitoring both plants and noticed it right away. So the browning was very small and only on the very tip of the leaves. After I noticed it, I stopped watering them with tap water. I collect and store a lot of rainwater to use for my carnivorous plants, because you can't use tap water on them. So I have more than enough of it in my reserves, and now use it to water both of my Dracaenas as well. Since then, the browning hasn't gotten any worse. If you don't want or have the spare time to collect rainwater, or don't live in an area where it rains that much, then you can buy distilled water fairly cheap at the store. But for me, collecting rainwater is the way to go. It's fairly easy, once you get the hang of it, and it doesn't take up a whole lot of time either. Plus, it's free. :)

I also needed to buy some bagged soil over winter and don't remember if it was a Lowe's brand or MG but it was much more chunky, and labeled for palms & citrus. It's the best bagged potting soil I've encountered, hardly any peat which, IME, is just stuff that helps me kill plants, not keep them healthy. I've been thinking about getting more since I like how it has 'done' so far, not compacting or getting hydrophobic, though I know the chunks of organic materials will decompose quickly in the Alabama weather this summer, just like mix that I create with bark/mulch/similar stuff. So, when using a potting mix with organic ingredients (can decompose into smaller bits,) know that it will become less and less hospitable for roots to thrive, because the air spaces are eliminated as the tiny particles sift into them, and the growth of roots squeeze the air out of the pot, necessitating repotting more often, I do this annually. A mix of ingredients that don't decompose, or decompose much more slowly can allow plants to go 2-3 years, generally, before repotting is critical - from that particular angle. I think woody entities stay more healthy if their roots are trimmed annually, but this can be a daunting chore for some larger plants. Not a 1-size-fits-all thing, or 1-sided issue, largely dependent on your style, schedule, budget, etc... It's also good to know that the soil you used has fertilizer in it. It should say how long that is expected to last. Adding more fertilizer before then would definitely be overkill for something as slow-growing as a Dracaena. Whatever one is using, don't pack it in the pot. Leave it 'fluffed' and full of tiny air pockets. The first few times you water, don't avoid being thorough, but try for a gentle sprinkle, so the motion and weight of the water doesn't compact the soil. This gives roots access to oxygen and moisture at the same time, necessary for them to be healthy, as said above. Not to put too fine of a point on the water thing, but aside from being unnecessarily expensive (if actually filtered in a way that it contains no minerals, fluoride, chlorination, etc...,) bottled water has a wide range of possibilities, including being tap water just like what comes out of your own tap. Also common is spring/mineral water, containing unknown substances that may or may not be appreciated by any particular plant. Once water hits the ground anywhere, it can contain various substances, like lime which can alter PH. Distilled, rain, and condensate from dehumidifier or A/C are sources of water with "nothing in it," assuming it's collected in a clean container.

What is in a pot does not matter, as long as it's not toxic to the plant in some way, just its' texture & ability to retain moisture & oxygen @ the same time. If it has no inherent fertility, very effective fertilizers exist to serve those needs. I don't doubt you at all. I don't have access to ingredients for that so I can't offer any feedback about it. If buying a bag, I look for cactus/palm soil, but go more by weight over what it says, and look for a broke bag to inspect and make sure there's no peat in it, and hopefully not much perlite. If it's not lightweight for its' size, it's not helping me reduce the weight of larger pots, and probably not going to help with keeping more oxygen in the soil. Digression alert, probably on this whole post... I don't want to be confusing either, and do not offer any of this as a recommendation because it has evolved over quite some time of trial'n'error, and other, personal factors like personal acute dislike of perlite & seeing those little white things in my pots, a lot of reading about roots & microbiology, dislike of spending much $ to have something in a pot in which a plant can grow, realizing that if there is no peat, I can probably keep a plant alive, ...and especially to someone in the middle of a city without a yard. I'll use anything but peat/potting soil, and often add some roughage from compost pile. Dracaenas grow fine in ground dirt from the "good dirt" part of a tended plot, especially if I'm going to repot them often anyway. Fine for smaller plants but way too heavy for a plant of decent size. Since all old "dirt" gets put into flower beds, I don't put anything in pots that I wouldn't put in/on the ground. This is why I quit buying flats of annuals to use in the ground and started putting my house plants instead, because I kept finding styrofoam instead of perlite in the soil of them. I refuse to bury other people's non-biodegradable trash in my yard.

Give it some time and hold off watering until the top of the pot is dry. If it's in shock there is nothing else you can do but wait. My experience comes from having many Dracaena over the years. Your plant may not look good for a while but I'll bet that it will perk up and keep on growing. These pants can take some cold but they do not do well in freezing temps. If individual leaves fall off that is fine, but if clumps get limp and soggy at the stem, that could be an indication of a total loss. However, even if every leaf drops off, give it more time. They have been known to regenerate when you think nothing is left. Do your best and love your plant. On the upside, IKEA is only a bus ride and a 20-minute walk away...but wait for a day that is at least 45*F. Good luck.