Why did the hunnic invasion lead to the Germanic people migrating west but the rise of Rome didn’t cause a eastern migration

I’m guessing that by the rise of Rome, you mean the expansion of Rome north and east into Gaul, Germania, Illyricum, Dalmatia, Pannonia, Dacia, etc. 

I think part of the reason is that the Romans actually didn’t push that far northeast; the decision to stop at the Rhine and the Danube limited the “push” factor eastward. Likewise, the Roman policy of trade and tribute, establishing client kingdoms in Germania, Dacia, Sarmatia, etc. created a buffer zone that could absorb eastward migration.

And sadly, I think another part of it has to do with the Roman practice of imperialism, that the focus was on conquering and then Romanizing people where they were as opposed to driving them off the land, but even more so the focus was on enslaving people, which meant that people who might have become refugees to the east instead moved south into the Mediterranean slave markets.