He is not considered a traveller

Reference: https://x.com/fwd_frd/status/1112438762028650497

لو كان للرجل زوجة في بلد، وأخرى في بلد؛ فإنه يكون في حكم المقيم في البلدين، لأن المرء فيهما مع أهله.
العلامة ابن باز | التعليقات البازية على الزاد ص١٢٦ pic.twitter.com/wIZ4ybsy5z

— فوائد وفرائد (@Fwd_frd) March 31, 2019

at-Ta’leeqaat al-Baaziyyah ‘alaz-Zaad – p136

Shaykh Ibn Baaz said:

If a man has a wife in a city, and another wife in a [different] city, then he is [legally] considered a resident in both cities. That is because in both cities, he is with his family.

Translation originally published on 2 May, 2019.