Since its internal matter between CIC and CBSA we may not know the exact time frame. Probably the CIC can access that data directly from CBSA's database. However, it all depends how soon CIC would review it, approve your case and schedule your Oath.
Let's hope and wish you get the Oath invite soon.
As a precaution, get thru ATIP your travel history from CBSA, it takes 31 days and from FOIA, USA in 6 weeks. Although, CIC get CBSA report but might NOT have access to FOIA report. Upon receipt, you can send copies of both to CIC as an additional solid proof.