For the first time probably ever I disagree with Javi
The Bowtech system works excellently with finger shooters as long as they are happy shooting with a draw stop. Which personally I don't like but I have set up Constirutions and other binary cam bows for finger shooters. I have shot a Connie with fingers but mine is set for a release.
Centreshot is different for finger shooters and needs to be set to start with point pointing about a points width outside true centre. A lot of people with some knowledge set it like a release which in my book is wrong. I have ended up there after a walk back tune but don't start there.
Where I 100% agree with Javi is spine is vital for finger shooters and you need a stiffer spine than a release shooter... another common set up fault.
I Am Shooting A Beeman Carbon Explorer 400 With A 100 Grain Tip At 65 Pounds
Unless you are shooting about a 26-27 inch arrow and at about 27 inch draw length you are too weak in spine is my first guess. I shoot 400 spine arrows cut to 28 inch at 65# with 80 grain points out of my Martin Slayers with fingers and this is pushing the spine to the limits and I am blessed with a clean finger releas and have always shot a slightly weaker spine than most.
Do some bare shaft tuning.
Start at 10 yards and when your bare shaft is tight with the group or ideally the lowest arrow in a tight group move to 15 yards and adjust again until you get this position then again at 20 yards and tune for a tight group.
Personally I prefer the bareshaft at the bottom of the group as this means my nocking point is a smudge high which I have found give me more forgiveness, kinda like some release guy like a touch high tear.
After bare shaft tuning try a "Walk Back" tune to confirm centre shot is good at all distances. This also is good for setting plunger tension.
To finish I group tune at 40 or 50 yards, if the groups are good and tight I leave alone. If the spread slighlty horizontally I adjust my centreshot fractions until the groups shrink. If they spread vertically I adjust my noking point fractions until they shrink.
Then I measure what I have got, make a note and leave alone as long as I am still shooting well. If my groups go to hell, I measure and compare with my notes and correct if anything has changed. If still the same, I put down to a bad day, 5 bad days = a retune!
Good luck and hope this helps!