I have observed toxicity using mKATE2 (Evrogen) in mamalian cell lines. Also they state that it is non-toxic. I don't know how similar mKATE2 and mTurquoise are.
The mKATE2 from Evrogen is mainly for tagging fusion proteins, so perhaps different in toxicity. Turquoise is not very different from GFP, but I know there are several variants of GFP, some of which are more toxic to mammalian cells.