It may just be fear mongering, or are they really coming in from Ukraine?
No - that doesn't happen. There would be no need to come to Poland that way, since anybody who wanted to could come in via Slovakia, Czech Republic, Germany which have open borders with Poland. With Ukraine, the border is tightly controlled. Most of the refugees who have entered Poland (not many) are en-route to Germany etc where the support structures are better.
Any migrants who come won't be in that region - there's little there to attract a newcomer who doesn't have an income. There are plenty of Ukranian refugees (usually though not always with some Polish roots) from the war zone in East Ukraine, however those people head to various reception centres run by the government, the Red Cross or the church and then either study (many are young) or move to places where there is employment.