So if an app installs an encrypted volume for which you don't have the password to, you go to jail? That doesn't make sense. How can they know if I have the password or not

They can't know, they infer. AFAIU, normally they just detain you at the airport and harass you to try to break you. To jail you they're technically supposed to be confident enough about you knowing the password to be able to charge you with a crime (presumably something like obstruction, possibly specific to immigration law, otherwise right against self-incrimination might prevent a conviction on failure to disclose alone), or have other evidence of some other crime. Then you end up in the legal system, where courts handle due process and a judge, preliminarily, and then a judge or jury decides if you knew the password.

Note that the recent high-profile case of a man being jailed involved him refusing to decrypt, rather than claiming he didn't know. He was deliberately trying to test the law regarding the permissible scope of inspection of digital data, to force the matter into the courts so the issues could be litigated in a controlled context untainted by other potential crimes; being arrested and charged was part of his plan.