This could be a consequence of erratic watering. Has there been a dry period followed by a wet one? This tends to happen when plenty of rain follows a dry spell. The lack of water causes them to dry up then when the ground gets wet again the water taken in causes the fruits to swell up too quickly and the skins split.

Make sure there is a consistent supply of moisture to your Plum tree by regular watering. Also, you could improve the soil by incorporating plenty of well rotted organic matter and a good mulch each spring.

I wouldn't overly worry as in mid/late june you will find the tree will shed plums [called june drop] as the plant regulates how much fruit it can carry. its an internal hormonal thing.

but as Myron said maintain steady watering.