Nowhere in the decision does the word vote appear. This decision is simply to answer the question about whether AA and US have a Single Transportation System and decide Craft and Class designations, which they fulfilled.
To certify the negotiating body is the next step, so after 30 days and once AMFA fails miserably, there will be a vote.
And yes, the unions have stated and implied there will be a vote. For instance on the IAM side they have a Q&A that goes likes this:
Q: Will the members only have two choices when the Alliance election is held?
A: Most likely, yes. When the Association applies for representation the choices will be for the Association or no union, unless an outside union intervenes and appears on the ballot.
OR from the TWU
"The first steps that follow the single carrier determination will be elections, at each of the three classes or crafts, that will determine the certification of the TWU/IAM Association for each class or craft. The Association will be certified when it receives a majority of the votes cast."