The refresh happens automatically. Find an aircraft in MyLog that has no details, but you know that the details have been autopopulated because you saw it being populated in the list (or you manually entered details using Database Explorer). When you run MyLog populate, you will see the mylog list refresh and the full details will be there.
A bit difficult to demonstrate really, but hopefully you get my drift. See the 2 attached shots of MyLog. I've manually updated the main database using Database Explorer to put in the details of the Hawk 43C554 and the AlphaJet short names. As soon as I use MyLog Populate, the details from NavData.dbe are populated to the MyLog list.