I'll just say that - with a particular focus on the term - "along with" can also mean
"in conformity or accordance with", implying that as long as the process is handled in its entirety or as intended, holding consecutive votes would be acceptable. There can also be a semantic debate about its usage as both a consecutive and concurrent descriptor in the same instance; "Along with my job of manning the election booth today, I also have to go by the bank at some point" would imply that these things are both happening today (concurrent), but could also imply that one will happen before the other (consecutive).
I believe I also missed the "immediately" part originally, which had I noticed that, would have rendered what I had to say moot.