We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters - no degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with a low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting and different cooperative jamming strategies. Specifically, our coding scheme combines several point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on a chaining construction to be able to deal with an arbitrary channel and strong secrecy. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.