In compatible relationships, the couple doesn’t have to worry about the relationship itself. It needs only a healthy amount of investment and attention to keep the flame burning at the same level. Instead, they can focus on whatever life throws at them in spheres outside of the relationship.
I think it's worth noting that if you've been through enough incompatible relationships, you'll worry about the relationship in a compatible one; at least at first. I've been in highly compatible relationship for over a year, but years of conditioning from past incompatible relationships cause me to occasionally fret over my current relationship. It definitely has gotten better with time, but it didn't just stop because of the relationship being compatible. My point being that worrying is often a personal issue, more than a relationship based issue.