@Tommy-D, not all verbs have double past participles – I think that might be what’s understandably confusing you.
The verb cansar is an example of a verb with only one past participle (cansado), so it doesn’t matter what auxiliary verb you use with it, because nothing will change. For verbs that have both a regular and an irregular past participle, the regular form should ideally be used with the auxiliary verbs ter/haver (forming a compound tense), and the irregular form should ideally be used with the auxiliary verbs ser/estar.
Only ter/haver ask for regular past participles by default. So yes, for any other auxiliary verb, including ficar, you can assume that the irregular past participle will be used (for verbs with double past participles) It’s the past participles that are classified as regular/irregular in this context, not the auxiliary verbs.
Concerning this sentence in Lesson 7, Double Past Participles,
O Ricardo foi aceite na equipa
according to Priberam Dicionario “aceitar” actually has 3 participio passodos: aceitado, aceite and aceito. How does that work? Why does this sentence not use aceito?