Doyle was transferred before this solidarity thing came into force, probably explains why Cork would not have known. Even if they had known they would have conspired to make a loss anyway :)
Having a quick read of this page
FAI page it looks to me that,
"Training compensation is paid to all clubs who've trained the player from age 12 to 21"
It applies only to cross juridstiction transfers and applies all down the line to all the clubs the player was registered to in Ireland
but "In the event of any subsequent transfer, compensation is only paid to the previous club."
I assume that means the last club the player was with before leaving Ireland.
It could mean the previous club in England, but that doesn't fit.
If it means the last club in Ireland, then that club is entitled to the solidarity payment for "any subsequent transfer".
All imho.
edit
there is also a calculation there at the bottom of the page
Solidarity Contribution - Payment breakdown
for age when at the Irish club and that calculation covers from age 12 to age 23.