It is needed to synchronize DNS zones using DigitalOcean DNS extension automatically.
Which settings should be done?
This functionality is not implemented in Plesk. Vote for this suggestion at plesk.uservoice.com.
The top-ranked suggestions are likely to be included in the next versions of Plesk.
To synchronize DNS zones manually go at Extensions > DigitalOcean DNS > DNS Management and click Synchronize all zones.