As far as I remember, only way to limit this on AIX is with ulimit.  Are you doing this as root or via sudo or some user?  If I remember correctly ulimit follows child process and this can create some funky stuff sometimes.  If you set ulimit for file to be unlimited (on client), then unless there is block at file system level (not sure if that is even applicable nowadays) I would suspect NW.  I remember with 8.0.x I could see that some commands on AIX were funky if file was more than 2GB (or 4) like nsr_render_log for example... perhaps calls used there were too old.  In 8.2.x they are supposed to use 64bit version so I assume all should be ok, but you never know.  You can try to do directed restore to some other box (AIX or some other UNIX/Linux flavor and see what you got; for example attach some NFS share and try to restore file onto it under some other AIX and then Linux box and see what results do you get).

I decided to reboot the client and noticed that /usr/tmp was missing so I created the directory and rebooted and now it appears to be working.

Not sure if the directory had anything to do with it but may have

I decided to reboot because setting the ulimit will only take effect after a log out, or so I read. So just wanted to be sure I logged everything out

Folder is irrelevant.