A year with no June storm in the E. Pacific could have interesting consequences. The last time it happened was in 1969 when Tropical Storm Ava formed on 1st July. That year was a big one in the Atlantic basin - 18 tropical systems, 12 of which were hurricanes, 5 of which were major hurricanes (including Camille).

Of course there are other years - 1995, in which there were only 10 systems for the E. Pacific, but the Atlantic had 21. Also, there was 1996, where there were only 9 storms in the E. Pacific, but 9 hurricanes and 6 major ones in the Atlantic.
If there is no storm in June it could be a signal of a busier year. But remember, there are still ten days left in June, and a lot can happen in that time.

Still looks as though we'll be going without a storm in the Atlantic this June.