You may get different views on this. Some will say not to fertilize newly planted plants but others will recommend to use root stimulating fertilizers. To be safe, wait two or three weeks after transplanting or if you see new growth before that then you may fertilize.
Look at the fourth post in the following thread giving some rationalization for not fertilizing immediately after transplanting and suggests alternative for providing nutrients:
http://forums.gardenweb.com/forums/load/newgard/msg082001174897.html

You do not want to put fertilizer into the hole when you plant a new tree. It actually can prevent the young tree from getting moisture up into the sap.
If you do fertilize in the first year, you could try foliar feeding and spray a solution onto the leaves.
The best thing to give a new tree is water about once a week or even more if you're having a hot summer.
Do not put granular fertilizers into the hole when planting.
a bit of osmocote may be OK cause it releases slowly and won't burn if you follow the label directions.

You could use blood meal and bone meal. Since they're organic the nutrients release slowly. I mix a cup of blood meal and 2 cups of bone meal into the soil I dug out of the hole before I replace it. I've never had any trouble with it.

I would not put any fertilizer into the hole. It is not a good idea to have fertlizer salts in direct contact with the roots. Even "organic" fertilizers can cause salt burn.

Blood meal and bone meal will not burn a plant. There are no fertilizer salts present. I use it in my seed starting mixes and potting mixes. I even start cuttings in potting mix with blood meal and bone meal added. I was told about the mildness of these by my county extension agency over 10 years ago and have used them ever since. If you can find it, rabbit manure is another soil addative that will not burn plants. If you use rabbit manure make sure it is dry because rabbit urine WILL burn plants because as it decomposes it makes a lot of nitrogen.

"Here is a good reference on fertilizer and trees that spell out the rates/100 ft square."

Boizeau, this is a site for landscape trees, not fruiting trees. Fruit and nut trees have different needs since they are using more energy to produce their crop. Organic fertilizers have to be broken down before they are usable by the plants and don't cause a salt buildup. Salt buildup is caused by chemical fertilizers. You are correct about soil preparation. It is very improtant.

Again I caution against putting fertilizer in the hole.
Fertilzers are salts, whether organic or chemical.
Nitrate is nitrate.
Phosphate is phosphate
Potash is potash.
The Main extension bulletin clearly warns not to do it.

Here is a link that might be useful: newly planted fruit trees

On another note, be wary of Ty Ty. They (and the other names they go by) are renowned for being shady.

For my fig trees, I usually mix a few handfulls of aged compost into the soil but not a lot. Most of my soil has been enriched over several years with generous amounts of compost, so this is not much different from the surrounding soil, just a little extra. I mulch with aged yard compost as well.

My newest fig tree was a King fig that I planted in a garden bed that was enriched with aged chicken compost, and it grew like crazy last year. Too fast growth can make it less likely to harden off in the fall, and be too frost sensitive, whcih might have happened with my new tree - I'll know this Spring. I think it's OK though. Also too much fertilizer can encourage excessive growth, at expense of figs, according to some authors.

I think that you are in uncharted territory with the Kricket Krap - I imagine that it would be like most other composted manure products, as long as it is well aged compost, should not be enough to burn the roots.

I also add generous amounts of crushed eggshells around my fig trees to enrich the soil with calcium. The soil in my climate tends to be calcium depleted, so the theory is that the eggshells will replace calcium. Figs are supposed to like calcium. A soil test might help you find out if you need any particular nutrients.

The linked site has some information about fertilizing fig trees, from the Georgia extension. It might be helpful.

Here is a link that might be useful: Univ. Georgia Fig Information

One trace element I've seen a favorable response to is boron, but most regions have enough, "I think". We are very deficient in the PNW. Our winter rains tend to leach the minerals out of the soils, and boron ends up in the Puget Sound, I guess.
Boron is usually applied foliar feed.