A Corporate Captain reported during landing roll they observed a departing aircraft from an intersecting runway fly overhead.

Narrative

On switching frequencies to ZZZ Tower; Tower instructed us to slow to our final approach speed. Our final approach speed is very slow in the C-680+ relative to airliners; and we don't believe that tower was aware of that or took it into consideration for their spacing. Our final approach speed is approximately 105 knots. We were on approach into runway XX; while airline traffic was landing on the perpendicular runway of XYR. Shortly after we slowed; my Co-Captain and I were observing the line of traffic headed into XYR; and saw that at our speed; we would likely be landing at the exact same time as the third plane observed on our traffic display. My co-captain suggested we increase to 120; and I agreed. We increased our speed to 120 knots. We observed that increasing our speed appeared to put us better between the landing airline traffic; which is what it appeared tower wanted. On about a mile and a half final; I slowed to our final approach again to execute the landing. This in turn decreased the spacing between our landing and the airliner landing on the perpendicular runway. My co-captain and I had already discussed the go around procedure in case we were instructed to do so by tower. We also discussed how we were going to land; due to the fact that we could see the airline traffic on final for their runway; namely that we would not be slowing down until we were through the intersection. We landed; and tower told us something along the lines of 'way to hang that one in there' which confused us; since we did what they told us to do. If we hadn't sped up; then we would have had a direct collision course with the airliner landing perpendicular to us. My Co-captain told me that when we went through the intersection on landing; he was 'looking at their belly' and after we were through; he 'saw their tire smoke'.Throughout the experience; I was expecting tower to instruct either us or the airliner to go around. When we had not received any such instruction by short final; we took it to mean that spacing was adequate for both aircraft; when in fact it was not. Had we been slightly slower; or had the airliner been slightly faster; we would have collided on the runway. If both had gone around; we would have collided in the air. If one of us had gone around at the last minute; there is a fair chance that our aircraft would have struck one another still. Tower should have provided more spacing between perpendicular landing aircraft. Additionally; due to the lack of instruction from tower; it seems we noticed the spacing issue before them. Had we received clearer instruction from tower about the order of landing traffic and what they wanted; this near miss could have been avoided.