As a EMHC, I can say that people do it both ways, but most have/take time to swallow first, so as to be able to speak their “Amen” clearly after hearing the proclamation, “The Blood of Christ.” Others, especially children, don’t seem able to swallow that fast, but manage to receive the Precious Blood without incident.
Since the Precious Blood is received via a tiny sip, during which one is very careful not to “backwash”, it is possible for some people to clearly and politely speak an “Amen” without having entirely swallowed beforehand (that is, so that they aren’t visibly “talking with their mouth full”). Either way can work.
As long as you know you won’t lose the Blessed Sacrament from your mouth by your method, as long as you can speak your “Amen” safely and reverently, do what works for you.
Whatever the case, if you need a few extra seconds longer to collect yourself properly than some seem to take, take the extra seconds you need. We’re not working an assembly line; we have however much time as reverence requires. (If you do a “dry run” with food of a parallel amount, you can show yourself that we are talking about a matter of seconds.)