Hello; To answer your question, no I have never kept that size tank in an apartment.
That said and at the risk of being a wet blanket I noticed a couple of possible problems when I looked at the picture.
First is the legs of the stand appear to be simple angle iron. I saw nothing to spread the concentrated force where the legs touch the floor. The weight of a 150 will dig those edges into most any floor except maybe cement. May I suggest some sort of metal pad of a few square inches between each leg and the floor. I guess plywood squares would work unless the floor is true wood.
Next thing is that stand does not appear to be stout enough from the photo. At the least check the mfg. rated capacity. Don't think I would put a possible 1500 to 1800 pounds on that.
I hope you got permission for such a tank from the building owner. I also hope you have renters insurance that specifies it will cover the potential damage both structural from the weight and from damage 150 gallons can do. If not you may face a lot of very expensive personal liability.
I hope you have already thought these things out and good luck.