During 1848-49 Poles participated actively both in the Revolution and in the following War of Independence. Their emigration greeted it wholeheartedly, they saw a possibility to expand the revolution to Galicia and then who knows what could follow (this is a rare "what if", what would have happened if we had won?, maybe we could have helped the revolution in Vienna?, and then the Italian uprising?, helping Poland gaining independence?). They organized the Polish Legion (Legiony Polskie) and every unit and every men were directed to there, this unit was used independently. Quite a few soldiers left the imperial army (Poles from Galicia served there) and signed up at ours.
Then in the next Polish uprising in 1863 the Hungarian emigration helped as they could, the homeland still suffered the opression which folled the revolution.
The Dualist Monarchy (Austria-Hungary) meant peace, and Poles came to find work. Some settled here, but most was just seasonal. Polish civil organizations formed here, Polish subdivisions were added to already existing ones (e.g. in the Alliance of Hungarian Lawyers). An important institution was formed, the Hungarian-Polish Society which became a focal point of deepening relations and organizing events. Ofc, these groups weren't just cultural or friendly, they often actively supported the cause of Polish independence.