Nobody except his formation director or perhaps his personal confessor has the right to tell him he has any issues, please.
Dear young seminarian, God bless you and our prayers for your vocation, studies, and formation.
I think the fact that you asked indicates that you have a feeling there might be something a little inappropriate with using the tabernacle in this way. Since tabernacles are usually blessed (I think there’s a prayer in the Rituale for it…) and have held the Lord’s body, I personally do not think they should be used for anything else, or really, ideally, I don’t think “private citizens” should own them. You might reverently wrap it up and store it someplace until you are able one day (God willing) to use it as a priest, or to donate it or loan it to another church. Even though you are putting holy things in it, it seems like a “profane use” to me.
You might indeed get into a little trouble at the seminary over it, so I would just get an ordinary container for your rosaries, medals, and things. I would just get one of those mini plastic sets of drawers (from Target or wherever) for the kind of for devotional things you mentioned. From what I know of these things, they look out for anything out of the ordinary in seminarians’ behavior - the question may be, “why have a tabernacle in your room?” If you feel like you can’t justify the answer, then I would not do it.
No offense to other posters, but my own personal impression was that some of them were a little unduly sharp when responding to you.