Caliber 240 vs. winder with gains of >30 sec/day

[MCMartiny]

I am experiencing a strange issue with my otherwise fantastic brand new 5712 (caliber 240 base) which worries me a bit.

I have an Evo Cube watch winder from Rapport London which so far have worked excellent with all my watches including my 5164 (caliber 324 base). The winder is of the type that rocks in approx. 90 degree semi circles instead of making full 360 degree turns. See https://www.youtube.com/watch?v=yFa6WIsY3vM

My 5712 is otherwise extremely precise when I wear it and well within the Patek standard of -2 to +3 sec/day. However, when I use the winder with the watch it gains double digit seconds per day, sometimes as much as 50 sec/day.

Has anyone else experienced problems with precision of a caliber 240 when on a winder of this type? Could there be something wrong with the watch? Do I risk damaging the watch using this type of winder?

Since I am fairly OCD about keeping the moon phase set I would like to keep the 5712 on a winder when not used. So can anyone recommend a small size winder (need to fit in my safe) that works well with caliber 240?