the databases can be used then only for educational / academic work (lectures, thesis, ...), not for paid projects, but that is about it. You can share the databases with students.
Obviously you also need to observe the license conditions for each database specifically, you can download them with the databases, and check that you have read them before the download. You should make sure that users at the university understand and follow these rules too. But this is the same for any database license, also commercial ones.