Alexis
a 1/4wave of coax or odd multiple 1/4waves transforms impedance whenever the load is not perfectly matched to the coax,
a short circuit at the far end looks like an open circuit at the analyzer,
an open circuit at far end looks like a short circuit at the analyzer,
if your antenna was 25ohm you would see 2:1 swr but impedance would be inverted to 100ohm at the analyzer,
a 100ohm load will be 2:1 swr & invert to 25ohm at the analyzer,
you can test this by putting resistors or 2 dummyloads on a t-piece at the end of your 1/4wave jumper,
if you do the same with a tuned 1/2wave of coax, you will see that the 1/2wave does not invert impedance when its not perfectly matched,
a 1/2wave reflects the load impedance at its input end,
both lengths will shift where you see resonance at the analyser`,
tune for minimum swr since minimum swr occurs when the load has least reactance.
i would use your best line isolator at the feedpoint & include it as part of your tuned 1/2wave jumper when you tune the jumper.