W/o hearing or seeing the bike is hard to know what is wrong, my best guess is that you have problems of tension in the cable or friction somewhere and the RD is just setting in the wrong place. Besides that is hard to know.
Not rocket science what is working wrong. Now if you can't really see any difference between a RD in the right place and in the wrong place then you deserve to pay for the repair
No idea what you call 1st gear, so there is even a slight possibility that you are crossing the chain big time. If thats the case then you found the problem, but again is hard to know w/o having the bike in front.
Good luck
