For the booking source to automatically populate on the reservations under OTAs below are the steps you need to follow:

From the management tab, add a new booking source if the booking source hasn't been set up yet. Click 'New Booking Source' then save the changes. 

 From the Channels section, click 'New External Channel' then choose the OTA from the selection. 

Select the OTA from the Booking Source drop-down menu and 'Save'.

Once this has been set any new reservation from the OTA will have a booking source on the reservation. 

Please note that you will need to manually set up the booking source for the existing reservations as it will only apply to new bookings.