Hilbert transformer's phase in .AC simulation
You have a linear phase because you probably implemented a causal filter. This just means that you have the desired phase shift of $-\pi/2$ plus a constant delay. The additional delay, which corresponds to a linear phase term, usually causes no problems. It is necessary to make the filter causal and therefore implementable.

The difference between an FIR lowpass filter and a Hilbert transformer is the phase value at frequency zero: it should be zero for a lowpass filter, and $-\pi/2$ for a Hilbert transformer.