Interesting.. I was expecting the problems with Z but not with XY like in your case. Really hard to say what can be the reason but here are my guesses.
1. Is your basemap in FM in the same coordinate system as your RTK service? It should be.
2. Do you create location profile in menu -> location profile? Create the one you are using for you map and RTK service so it maps correctly. If not set correctly, you wouldn't be able even to open the service (errors says something like location profile error, don't remember).
3. Antenna height should be set in the FM as pole height+0.13 for emlid.
4. Important! Once you press "+" to collect the point in FM, you are capturing the coordinates of the location where you pressed "+". Even if you move your receiver, it still captures and sends the coordinates where you pressed "+". My rule of thumb is ALWAYS press "Update point" before submitting. Could this be the reason for mismatch in horizontal in your case?
4. FM uses global EGM96 geoid model and I always get slightly different values for ortho height compared to the local geoid model even though my RTK receives the correct height from the base. I wish field maps have the option to select custom geoid.
In general, we use custom python script to convert and calculate the ortho height by using the ellipsoidal height from the receiver and the local geoid data. It is pain in the *ss but we do not have another option yet.
Do you need to do averaging? If not, 5 sec is enough in our case. Try measuring raw values without any post processing over some known point and compare. If everything is set correctly you should only see a slight difference in vertical and not horizontal. Check if both emlid flow and field maps give the same ellipsoidal height (altitude in FM) and horizontal.
