Transferring DNS to NameCheap: Does this take my website down?

Sorry for the simple question—I can’t seem to find the answer.

I recently transferred my domain from my IXWebHosting to NameCheap. However, in order to have access to subdomains/email forwarders, NC customer support has told me I have to transfer my DNS to theirs.

I’m just concerned that by doing this my domain will not lead to the website, since the files are still hosted on IXWeb. I guess my confusion is wondering how my domain will reach my files, if they’re being linked to a different DNS.

Since this can take up to 72 hours to fix, I’m trying to make sure this is correct, as it’s the website for my portfolio/resume.

Thanks!