I think the key word is "floating". This isn't a floating floor, it's a naildown. I don't believe it's going to be nearly as effective in a naildown situation, as most of the noise that is "muffled" in a floating situation is from the fact that there isn't good solid contact with the subflooring, as in nailed down. WHen there is good solid contact with a subfloor, the majority of the noise produced is from the reflective (rather than absorbtive) nature of the hardwood surface itself. Sound just echoes more into the air from a hardwood floor than it does from a sound absorbtive carpet floor. No amount of underlayment is going to alter the nature of the sound echo produced because the flooring is a hard floor product and not a textile based flooring product. It may be possible that installing a manufacture approved for naildown installation sound barrier can help with some of the percussive sound transmission from floor to floor, but it'll never be as quiet downstairs as if carpet on padding was the second floor material. And, you'll still get sound echoes upstairs that travel through the walls and open areas, simply because the wood surface reflects sound. You can't alter the basic nature of a hardwood floor. You can use rugs and additional soft furnishings to moderate the sound absorbtive properties and mitigate some of that reflectivity, but you'd have to practically cover all of the rooms wall to wall with rugs to make it be as quiet as carpet could be.

Use silane based spray foam adhesive. The foam will expand in the gaps and put your squeaks to rest. The silane based will stay flexible and will not break in the future. Avoid using polyurethane adhesives, the product is too brittle when dried and can break off in the future. Titan is one mfg that produces these type of adhesives.

My concern is whether or not the rubber is meant to be used as underlayment for flooring. The edges of the rubber seems pretty rough to me. Are they new? How long have they been hanging out in a dusty environment? Do they have an odour? Some of these rubber products will give a nasty odour for years and years and years. The flooring underlayment is specifically made to ensure this does not happen. And the odour, even if it is mild right now, will get MUCH stronger as the space warms up (like in direct sunlight, etc). And then there are the asthmatics out there. There are MANY people who are chemically sensitive to rubber particles that are left to float in the air. Again, the flooring underlayments made of rubber are specifically made to reduce the deterioration of the product to a minimum. And I won't get into the group of people who are allergic to latex (created from rubber trees that are almost exclusively used to create these rubber products). Someone who is allergic, specifically, to latex will be hospitalized after walking through a room with rubber underlayment...even the stuff that is specifically created for flooring underlayment. Their allergic reaction will be much worse if it the rubber underlayment used is not specifically designed for flooring. If you wish to continue, nailing through a rubber underlayment that is designed for this, should be no problem...I would find out if you need to glue down the rubber before you lay your hardwood. That's when some nasty chemicals can be involved. Rubber doesn't like to stick to anything. Which means the chemical make up of the adhesive could be quite nasty. There are several eco adhesives (Mapei has a few) that are created for rubberized underlayment...but they are hard to find and expensive ($1-$2/sf...or more). First things first: warm up the rubber (put it infront of a window for a day...let some sunshine hit it to get it to warm up) and then see if you like the smell. That should would be my first test...as someone with asthma and migraines...and a latex sensitivity.

So appreciate receiving feedback It means a LOT to me. God Bless all who have offered their expertise. This was a replacement cafe type door. That is there is a door on either side of the frame that meet in the middle when closed. I see now that with this replacement door there was a space between the tile and the door frame and he filled the space with grout.. Now there is grout between the tile and the door frame and there is some grout under the transition wood piece. Could this be the problem ? I am hesitant to call him back because I am not sure he is familiar with tile/wood flooring. He is primarily an outdoor contractor (septic systems etc.) who does indoor work during the winter. I cannot imagine another busy contractor would be willing to do this small (but important project). Neither my husband nor I are handy.