By "transmission tune up" I presume you mean a fluid and filter change? Likely one of the filters is not installed correctly.
Changing the fluid and filters should not cause a trans to get screwed up, UNLESS one of the filters (usually, the main sump filter) is installed incorrectly. The RFE transmission has two filters: the main sump filter (which is flat and has a snout that sticks up into a bore in the pump housing), and the spin-on (cooler return) filter (which is similar to a spin-on engine oil filter). Here is how to do a filter change the right way:
For the main sump filter: The key is getting the seal (that the filter snout goes through) right. Remove the old filter (there is one retaining screw at the rear of the filter, then you just slide the snout out of the seal). Then check the old seal to see if there are any cuts or nicks in the seal lips. Tug gently on the seal to make sure it is still tight in the pump bore. If the seal is OK (and still snug), then LEAVE IT THERE are re-use it. The filter will normally come with a new seal, but you can scratch the pump bore removing the old seal, and it is VERY easy to misinstall the new seal, so it's best to leave the old one in place if it's OK. If you do replace the seal, use an appropriately-sized socket to tamp it into the pump bore. The metal flange on the seal should be FLUSH against the pump casting ALL THE WAY AROUND (not tilted in the bore). Do NOT simply slide the seal onto the filter snout and then shove it into the pump bore; that will NOT work! The seal must be tamped into the pump bore, and then you push the filter snout through it. Do NOT leave the old seal in place, and then ALSO put the new seal onto the filter snout! Two seals will not work either! Simply push the filter snout up THROUGH the seal (not just resting against it), and THEN install the retaining screw.
Note that (for 2009 and prior) there are two different sump filters (one for 2WD models and one for 4x4 models). Make sure you get the correct one. Mopar filters include an instruction sheet (with pictures) explaining the differences. Make sure your new filter looks like the old one. If you get the wrong filter, the bottom snout (the metal inlet snout) will crash into the pan, and you will not be able to install the pan (so it will be pretty obvious something is wrong). For 2010 and later, all models use the same (4x4-style) main filter, and a common oil pan.
The spin-on filter has a threaded plastic snout that screws into a bore in the case. Install it just like an engine oil filter. Spin it on BY HAND until the gasket touches the case, then turn an additional 1/2 to 3/4 turn. Do NOT overtighten it, as this can crack the plastic snout. Just snug it up securely, by hand. We have seen some issues (delayed engagement, caused by torque converter drainback) associated with aftermarket spin-on filters (the filter includes a diaphragm that normally prevents drainback), so using a Mopar spin-on filter is recommended.
The pan gets resealed with RTV silicone sealant. Run a small bead all the way around the pan, on the TOP (flat) surface of the pan (not running over the edge into the radius going down into the pan), and running it around the INSIDE of the bolt holes. Bolt the pan on. Measure how much oil you drained out (usually it's about 7-11 quarts, depending on how long you let the trans drain for), then add that much new fluid back in (down the dipstick tube). Then start it up, shift through all the gear positions (ending in Park), and check and adjust the fluid level. NOTE that you must WAIT several minutes (I would wait at least 5 minutes) after adding fluid down the dipstick, since it takes a LONG time for the oil to run down off the inside of the tube, and in the meantime you will get a false (high) reading as the oil gets smeared on the dipstick. So fill it, then go take a break, have lunch, etc. and then check the level. Also note that the holes in the dipstick will be full of fluid if the level is at or above the hole, so it the level looks high, make sure the holes are full. A "high" reading with empty holes means oil is smearing on the stick (and is not actually high).
Any fluid that is labeled as MEETING the ATF+4® spec will work fine. Do not use fluids that are marketed as "replacement for" or "compatible with" ATF+4® (etc.). Some dealers stock Mopar ATF+4® in bulk (55 gallon drums). Last time I checked, this bulk fluid (sold by the quart) cost $5.15 list per quart. So you could check with your dealer and see if you can bring your own jug and buy some that way. The part number (for one quart of bulk fluid) is 68055894AA. Or see if you can find ATF+4 cheaper at your local parts store, Wal-Mart, etc.