Can water penetrate a slate roof that is in good condition?

My question boils down to this: Can water penetrate a slate roof that is in good condition?

Background...
We just had our slate roof and underlay renewed.
The house is in Oxfordshire UK and built in 1905.
The new underlay is Boost'R Hybrid Roof by Actis - installation instructions here: https://www.insulation-actis.com/fi...ROOF-installation-guidelines-PZ725-102018.pdf
I was expecting the roofer to install the underlay over the eaves tray (as per the text on page 4 and the diagram on page 5 of the above instructions).
But the roofer installed the underlay under the eaves tray and over the over fascia eaves vents.
This means the underlay comes down with the pitch of the roof then rises up to go over the "lip" created by the over fascia eaves vents just before the edge of the roof - see attached image.
I am concerned any water running down the underlay will pool in the area behind the lip instead of running straight out to the gutter.
The roofer says there is no problem as no water will get through the slates, and in the past slate roofs did not have underlays and they did not leak.
Is the roofer correct or do I need to ask him to change the design so any water running down the underlay will go straight to the gutter and not pool in the area behind the lip?

I am aware that in the past mortar was used with slate roofs. Is it possible his justification of "in the past slate roofs did not have underlays and they did not leak" only applies if mortar or some other characteristic (not in my roof) is present?

The slates are Gallegas 39 by CUPA T1 Slate 5mm x 500mm x 250mm

Many thanks in advance.

Well he's partially right that many older roofs do not have an underlay and also do not leak.

However there ought to be a continuous tilting fillet to prevent the sag you're seeing. You say he's fitted the underlay beneath the eaves tray but we can see the underlay on top?

Yes, the underlay is beneath the eaves tray - I have attached an annotated copy of the image to clarify what its showing.

Think your terminology is wrong there, underlay is the roof membrane, which is correctly laid over the top of the eaves tray. What is lacking is the tilting fillet, the solid timber wedge shape bit of timber that would sit under the eaves tray/membrane and prevent this sag. Obviously the battens on top of the rafters will have to be cut back to accommodate it.

The underlay should be over the top of the eaves tray, as you suspect. The counter battens will need to be cut back to accommodate it.

denso13 said:

The underlay should be over the top of the eaves tray, as you suspect. The counter battens will need to be cut back to accommodate it.

Click to expand...

The underlay is over the top, his terminology is incorrect.

Where have you found this novice?

freddiemercurystwin said:

The underlay is over the top, his terminology is incorrect.

Click to expand...

Not according to his photo, he lifted the eaves tray and took it. The annotated photo clearly shows it on top.