Yes, Puffins will probably be gone. I know you've been to Iona but all the wildlife tours you can do will mean you have to go back to Craignure on Mull, then either down to Iona or across to Tobermory.
I don't know if Rick's tour just does the road down to Iona from Craignure or the whole island, but something like this sounds right where you get off the boat and travel across Mull to Tobermory for your boat-
EDITED FROM PAM'S COMMENT- So this trip perfectly compliments the one on the tour in allowing you to see the other end of the Island and the colourful (literally) village of Tobermory.
Other companies do broadly similar trips.
Due to ongoing construction work you won't be able to land on Staffa. I don't know how West Coast Tours or the other boat companies are handling that- best to ask them before booking.
If you would like a walk, why not take the 0700 CalMac service ferry to the Isle of Coll, with almost 3 hours ashore (while the ferry goes to Tiree and back), arriving back at 1510;
or CalMac to the island of Lismore at 0800 or 1100- both options give you 3 hours on the island, 55 minute ferry ride each way.