You should never lay natural stone steps onto asphalt Because it will expand and contract with temperatures and move the stone above it
You should therefore Remove the Asphalt and waterproofed steps with various other methods before you lay natural stone on top

You should never lay stone onto asphalt.
Asphalt will expand and contract overtime resulting in the stones moving and therefore not bonding to the floor.
Natural stone should also never be laid on a cement bed, i'd recomend a NHL 3.5 hydraulic lime mortar using the stone dust and lime at a 3:1 ratio. But if im honest it sounds like you need a professional to complete this work if you want it done to a reasonable standard.

In response to hertstone and Jb masonry,please research before you give wrong advice.Thermal movement in construction is a good place to start.You don’t say weather it’s internal or external.most materials can be bonded but the amount of expansion and contraction needs to be factored in.expansion joints for example.Most big modern building construction consists of a steel frame and cladding and is fixed so the building can flex.There are a lot of products on the market for bonding materials,low modulas mastics and flexible adhesives are probably your best option and possibly use ditra matting and it should be fine as these products are designed to overcome problematic substrates .the pointing all depends on the stones.do some research but you’re best getting a professional in .it’s worth every penny you only get 1 chance to get it right.laying on just stone dust and lime will 100%shrink and fail.if you are going to use mortar it should be a clean well graded sand which means it contains aggregates of all different shapes and sizes so they lock together.never just stone dust!Jb look into historic mortar