Houve uma entrevista logo após Spider-Man: Homecoming, onde Kevin Feige confirmou que esse Spidey tem o senso de aranha.
I recently asked Marvel Studios president and Homecoming producer
Kevin Feige if the Spider-sense exists in the MCU or if the need for
such a super-power was negated thanks to Spidey's costume now being
decked out with AI and other Stark tech that aids him in exploring his
surroundings.
"No, I think he has it. And I think he has it with or without that
suit," Feige told IGN. "I think how we explore it in a cinematic sense
will change. I mean, that was sort of a big showy part of previous
versions and we thought that we'd make it more of an internal, sort of
second nature thing for him."
Feige continued, "But there are ways coming up that will slowly hint
at that and also just make it part of his, you know, his natural
abilities. But we don't know that if it will be -- I think we'll
explore it further down the line, but [it's] definitely him not the
suit."
Se for esse o caso, podemos concluir com segurança que esta versão do Homem-Aranha faz realmente tem o senso de aranha.
Portanto, por extensão, seus "reflexos" na Guerra Civil certamente seriam um resultado do sentido da aranha.
Até o momento em que pude pesquisar, não encontrei nenhum comentário específico sobre essa incidência na Guerra Civil.