A lot of players(including me) have to wait some time, or even reboot before they receive the adventure tab after accepting the invite.
I found that if u use few refills on your mines AFTER u accept the invite, u will receive the tab in 20-30 seconds max( probably when u use refills u force your island to update).
I hope this will help!
Yup, sometimes opening trade and then history tab works too, mail and outbox also works sometimes. Didn't know about the refils.
Or stop and start a well.
I was also refreshing the game but found that stopping and starting a well worked too.
You can also use a buff, I keep stack of fish platters for this reason alone :)
Also ideal for that old tat the explorers bring back sometimes :)