Forgetting the underlay

Hello!
We have the following problem and need help: One year ago, we had the pitched roof of our house insulated by a professional roofing company. Now, condensation has repeatedly formed on the vapor barrier. Since nothing changed, not even when we altered the ventilation behavior, I cut open the vapor barrier at one point as a last resort: A cold draft came towards me. Some gaps were present between the insulation boards, while in other places the insulation boards were compressed between the rafters (probably cut too large). An underlay membrane, although listed on the invoice (and paid by me), was not present. Through the gaps, you could see the tiles.
Now the question is: What should be done? Although I am an amateur, I suspect that gaps and compressions in the insulation boards are not okay. Does this need to be remedied? Or is it sufficient to spray insulating foam in between and close the vapor barrier again?
And: How important is the underlay membrane? That is, is it enough to demand the calculated amount back from the roofing company since it was not installed? Or should something structural be done here?
Drywall and painting work are now almost finished everywhere, and the rooms are inhabited. If the underlay membrane is necessary, could it also be installed from the roof side? After all, there are 74 sqm of roof area.
I am puzzled by the whole matter, as the master roofing company that also carried out the insulation work is considered absolutely reputable.
Thank you all in advance for the answers.

Did the executing company plan the measure itself? Has it been officially accepted by you after execution?

Otherwise, I would refuse acceptance here as long as the construction is not described in detail correctly and checked for building-physical consistency:
- Insulation boards between the rafters are not common. Intermediate rafter insulation is always flexible and adapts to the rafter intermediate space. Insulation board sounds like EPS/XPS and would rather be the wrong material in this place.
- There is definitely a lack of a vapor-open, windproof underlay or under-roof membrane, depending on the roof pitch and roof covering, as a second water-carrying layer. It also prevents the insulation from being flushed/blown through by outside air, which can fundamentally greatly reduce the insulating effect. It must be installed. This is only possible from the outside.
- The insulation must of course be installed continuously without gaps.

The entire measure does not seem to have been carried out professionally. Master companies are not automatically a guarantee for this. Such construction work must always be designed, monitored, and accepted by an independent party.

Thank you for the quick and above all very helpful response!
Insulation board was the wrong term; what I meant was insulation wool cut to fit as boards. - In fact, the company planned the measure themselves and also provided for an underlay membrane. It was supposed to be installed from the inside on the rafters. And the company also charged for the underlay membrane on the invoice with just over 700 EUR. Therefore, I was very surprised when I opened the vapor barrier today and saw a gap through which you could directly see the roof tiles (see photo). The acceptance by the energy consultant is still pending, so this is my preliminary inspection and inquiry to already know what to expect.
I placed my hand in the gap; the tiles lie directly on the insulation (with no distance). If I see it correctly, the matter is clear: the roofing company must subsequently install the underlay membrane, and then from above.
One last question: Could the insulation already have been damaged due to the unprofessional work?
Once again, many heartfelt thanks for the help!

As it looks, there is only the battens on which the roof tiles rest. However, the so-called counter battens are missing, which are screwed directly onto the rafters in the rafter direction and form the ventilation layer of the roof covering. The underlay membrane/roofing membrane is installed between the counter battens and the rafters. If the ventilation layer and the second water-bearing layer are missing, the insulation cannot simply be installed like this. The construction would then have to be made vapor-tight on the inside, which in reality does not work 100%. The entire roof structure should not have been executed this way but should have been fundamentally constructed differently. If the roof is to remain without a ventilation layer because you do not want to have it reroofed, there are constructive "tricks" to carry out the interior expansion. However, these are more expensive and must be planned from the beginning in connection with the overall expansion situation of the roof. Have these details worked out by an independent planner. Craftsmen are not planners.

The insulation already installed may possibly already have an increased moisture load and have lost some of its insulating effect. Glass wool or mineral wool only release moisture diffusively and not capillarily. Drying out takes correspondingly longer. If drying cannot be awaited, the insulation may have to be replaced.