"Every nonresident with Oklahoma source gross income of $1,000 or more is required to file an Oklahoma income tax return". Reference: https://www.ok.gov/tax/documents/511NRPkt-18.pdf Note: there's no 60 day requirement, only the $1000 income.
The wages you earn, telecommuting from OK, are OK source income, for the $1000 threshold.
The "60 day alternate address" is probably an employer "thing" and has nothing to do with your requirement to file an OK return and pay OK income tax. It may be an OK employer withholding requirement. You'll have to ask them.
