If it is biannual it would be the first plum or cherry I heard was biannual. AFAIK it is not biannual. Since 2 reports from Zone 9b and 8b one possibility is that it is very high chill. Also waiting 4 years for fruit would fit the profile of many sweet cherry trees. I have waited as long as 6 years for sweet cherries to produce. It took so long because conditions were rough and it was slow to size up. 6th leaf it produced, and produced well. That was a Glacier cultivar. My Whitegold sweet cherry only gets about 1/2 day of sun. produced 1 cherry third leaf (about 30 flowers). 4th leaf if produced about 20 (70 flowers). Now this year it’s 5th leaf. If your tree is not in full sun all day long, expect it to have to become bigger to produce.
I would also like to add that if you don’t thin properly and let your trees overbear, I can see a plum having minimal fruit the next year.
Having said that it is possible this tree is fussy. It might not be the best fit for many. If you can’t grow sweet cherry very well in your area, you might not be able to grow this tree.