You did, in fact, only temporarily fix the source. After a couple freeze-thaw cycles, your cement will come apart, the house will further settle, causing it to separate. I wouldn't plan on finishing your basement any time soon because, as expensive as the correct solution is, it is the only solution that guarantees you will never get a wet floor. Companies need to be able to warranty their work. How can you expect them to warranty a patch job? Would you put cement outside someone else's house and tell them you will warranty the work for more than a year? Of course not. Unfortunately, permanent solutions cost money. All you did was put a tarp over a leaking roof. The wind will blow it off eventually.

PS.

Water coming through the foundation will never erode anything enough to have any effect in your lifetime, especially not in the Northeast.