Are you preparing the medium or you buy it? If you buy it you should not find crystals (perhaps are they cell aggregates instead of crystals?)

DO you inactivate the FCS? by heating?

On the other hand a more convenient medium is RPMI-1640 Medium 

Hi Augustine, Rafael is right. Your cells are lymphoid and grow in suspension. They they do not require the elevated levels of cations (nor glucose) that are present in alphaMEM.

Crystals in cultured cells are usually precipitates of proteins / peptide aggregates and/or phosphates. The high levels of cations and sugars in aMEM are more likely to result in peptide/phosphates and even urate crystals than you would find in RPMI-1640. FYI RPMI-1640 was specifically designed to support the cultivation of non-adherent lymphoid cells!

That said do not simply switch over to RPMI. You need to wean your cells across. Have a look at Ian Freshney's The Culture of Animal Cells on this subject. 

http://bcs.wiley.com/he-bcs/Books?action=index&bcsId=5959&itemId=0470528125

Are you using a humidified incubator?  If so, is there water in the pan?  I have seen similar crystals when someone forgot to add water for a long time and the media osmolarity was going through the roof. 

I also have seen instances when inexperienced people have mis-identified fungal contaminations as accumulations of salt, but the crystals you described would be highly unlikely to be fungal.

Finally, I also have seen inexperienced people confuse dehydrated salts on the underside of culture plates as contaminations inside the plates.

I found the same problem , i use RPMI 1640, when i added NPS2143 "calcium sensing receptor antagonist" at high concentration 25um and 50um , crystals was formed 

It was needle like structure