Shower – Slow drain after tub-to-shower conversion

I recently hired a plumber for a tub-to-shower conversion into a first floor (slab) master bathroom. I had already removed tub and demo'd the walls, so the scope of work involved:

1. Extending existing copper lines up into exposed wall for shower valve/head
2. Add 2" PVC drain/p-trap in center of shower (including slab work and new concrete), coupling to existing 1.5" drain inside slab (using Fernco coupling)

Number 1 was pretty straight forward. Number 2 was also straight forward, although I wasn't sure about the Fernco to adapt the 2" PVC to the existing 1.5", but he assured me this was standard practice:

I was happy with how everything turned out initially, and after tiling we started to use the shower. But we noticed something strange: for the first minute or two, the water would not drain fast, and would start to puddle (~1"), but then all of a sudden all the water would drain and it would stay that way for the duration of the shower (ie, no puddling at all near the drain). It has been about 4 months and now the 'puddling phase' lasts more like 4-5 minutes and gets deeper, but then, like magic, it all suddenly drains. We used the bathtub as a shower for years and never had any drain issues.

Other things to mention:

• There was no roof vent for the bathtub, but it did have the standard stopper assembly so this could have acted like a vent?
• The original drain in the slab is about 48" from main sewer line (toilet), which has a 4" roof vent.

My main questions are:

1. Why does it drain slow at first, then suddenly drain normally?
2. Did the plumber use proper technique, ie, the Fernco?
3. Is this a vent (lack of) issue? (If so, I'm screwed)

Thanks for reading.

UPDATE (01/25/18): I have contacted the plumber who did the work. I told him about the "double trap" theory, which totally makes sense to me. However, he is not yet convinced as he says he "has done hundreds of tub-to-bath conversions and never had any issues if there was a tub trap in the slab." He thinks it is some type of obstruction in the line, and will come out and run the line to try and push out whatever might be in there. My engineering/physics mind makes me less optimistic than he is, but I hold out hope since it is, by far, the easiest solution. Fingers crossed, and I will update soon.

Another UPDATE: The plumber finally came out (he was battling flu). He contended that there should be no problem with having a new trap as part of the shower drain which feeds into the slab where there is (presumably) another trap…as long as there is a down-stream vent, which there is. However, I was really skeptical since what Josh said below made sense from a physics point-of-view. His thought was that there was simply some blockage somewhere; which again didn't make sense since the water drains well after running for a few minutes. He proceeded to use his auger to try and clear out the blockage. Well, we were all very surprised when he pulled out a 4" piece of 1/2" copper all wrapped up in a big hair-mess. WTF? It must have fallen in the drain when he did the original work, and the only explanation to why it drains well after a few minutes is that it somehow "floats to the top" or whatever and gets out of the way. Not sure we'll ever really know why, but now the system drains well, no problems at all. I don't really care since I won't have to redo things to fix it. 🙂 Just thought I'd post in case anyone comes across this and wonders about this same type of problem.