Hold-over tenant in California willing to pay 2 weeks of rent. If I accept rent, am I now in a month to month tenancy?

The tenant's year lease is about to expire. The tenant pays rent on a monthly basis. I do not want to extend the lease. The tenant is not moving out at the end of the lease becoming a hold-over tenant. They claim they need an extra 2 weeks to move out and are willing to pay the 2 weeks in rent. My concern is that at the end of 2 weeks, they may not move-out. I have read online if I accept any monies (even 2-weeks of rent), I have just entered into a month to month tenancy which then would require me to provide a 30 day notice to move out. This would delay my ability to file an unlawful detainer. Is this true?