Is syncronization bidirectional with IMAP accounts?

I'm having a lot of trouble with moving my years of POP mail accounts to a new computer using IMAP. I'm starting with my mail AOL account but Synchronizing TB the web account folder structure just isn't working. My initial installation went fine, but I can't seem to modify the folders and use message filters. The initial installation basically duplicated the web account folder structure automatically, but making modifications isn't working. I can't even delete test folders I set up on TB. I select them and try to delete, but they never are deleted. On IMAP accounts, how does the sync work? My pop email has stopped collecting email, so I guess there is no turning back at this point.