That is clearly not a universal thing, as my KFC225 will capture a glideslope from above or below - so long as one is reasonably close.
And many years behind a KFC 200 a/p is my lame excuse for not knowing the SOPs and limitations for my current aircraft.
But here we are talking about an LPV glideslope, not an ILS one.
Would you expect a difference? The initial parts of an LPV approach are flown in GPSS mode, but the final approach segment is flown in NAV (APR) mode. I get the impression the a/p treats the LPV CDI and GDI just like an ILS, which probably means that having flown the first parts as if on rails, it starts weaving all over the place.