It's my own opinion, and should not be considered legally. However, I would guess if you get paid from the Alberta company, and the company's entitlement is under Alberta registration, you should be okay.
I had a similar case when I applied for AINP: my company HQ is in Toronto, I'm working in Alberta, and the mother company is in Calgary. My payment is coming from Toronto office, but the company entitlement is in Alberta. My contract and collective agreement is under Alberta registration. You think this may be complex? After all, I was determined to be working in Alberta.