This cohort is an example of:
MM rulebook p.11 wrote:
A few cards that can be used on checks don’t use any of your skills; they instead specify the exact dice you need to roll or the result of your die roll.
This case is covered in:
MM rulebook p.24 wrote:
Blessings...If a card instead specifies the exact dice to roll for the check, the added dice are of the type specified by that card.
So, a blessing played on a combat check which Balazar is making using Padrig adds a d10, or a d12 if Balazar has a role card.
Your second example is not analogous. The player is making a Divine check. Their skill die is a d4. So a blessing adds a d4. (In the first case, Padrig specifies the die which is used instead of a skill die for the check. In the second case, the ally is adding a die, not specifiying the skill die.)