The supplier of materials should be generating an SDS in which Section 5 would describe suitable and unsuitable extinguishing media.

You need to follow the fire triangle "Heat, Fuel, Oxygen" where if you remove one the fire stalls.

Powder smothers fire by creating a layer which stops oxygen contacting the fuel.

CO2 smothers fire by displacing oxygen from reaching the fuel.

Water removes heat cooling the fuel (you are trying to get the bitumen below its flammability temperature)

High pressure water jet would be inappropriate as there is a potential to lift and distribute hot bitumen- however water spray would shower the fuel in a cooling effect.

IMHO CO2 will blow away the powder negating any benefit from its use and does not cool it is merely a feature of the compressed gas during expansion from being released from being stored under pressure.

Suprisingly CO2 has very little cooling effect. It will extinguish a bitumen fire for a moment, but re ignition is highly likely.

For bitumen covered felt, foam or powder would be my choice but not both. Powder of course may well blow around a bit at roof level, even on the first floor.

Foam will deal with the oil based bitumen and as its water based (nearly all water) it will deal with any timber surfaces alight under the felt - if it can reach it. There might be some initial flare up as the foam hits the bitumen, but this will die down if the foam stream continues

The most important thing is ensuring the crew keep their escape route available and do not box themselves into a corner away from their ladder whilst chasing the fire across the roof!!!

To confirm this is for bitumen felt fires and not a bitumen boiler where 9l or even 18l of  foam would not be enough and must not be applied. In these cases, drag the lid on the boiler to partly smother the fire and dial 999

toe: I agree with you that in 98% of cases, an emergency plan should include that the fire service should be called simultaneously or before firefighting has started. This is especially so for a roof fire like the OP's example.

Roof fires can spread very rapidly. Lets not forget that roofing materials &/or the roofing structure in in place to stop rain reaching under it. Therefore if the fire, embers or heat has got below the roof, no amount of portable fire extinguishers will reach it and you are wasting valuble time chasing the fire.

No fire service in the UK will grumble about being turned out to a fire that has been extinguished before their arrival. But they might not be too happy if you delay calling them and, like in this example of a 999 call delayed by 35 mins, it all gets a bt out of control!!  

https://www.bbc.co.uk/news/uk-england-hampshire-49071456