Walking my dog and he lets turds slip out?

Hi,

We recently moved and my dog no longer has a yard to utilize for restroom breaks. He hates and almost refuses to use the bathroom on the leash. He will wait to go until he goes to daycare. Recently I’ve been finding random turds around just one not a pile. Today I took him outside and on the walk I saw the turd slip as he was walking. It was solid and then 2-3 mins later he gave in and took a proper dump. Is this due to him literally holding it until he can’t any more and they slip out?