I also agree as far as the Progress Party goes, they are a different thing compared to SD. But what is PS except stricter immigration, anti-EU, and anti mandatory Swedish in Finnish schools? Besides the mandatory Swedish thing, those are the exact same pillars as SD stands on. I doubt that there is anyone who really votes for Soini except for those issues. And I'm aware that PS casts itself as the defenders of the welfare state and the working man and what not., but so does SD. That's (as you noted) hardly the reason their voters vote for them.
There are actually plenty of people who voted for PS because of welfare issues and rural issues. Take for example, the party's strongest municipality, Kihniö, where the party got 53 percent in 2011 and 48 percent in 2015. Almost all of that is support for a former Rural Party (Finns Party's predecessor) politician Lea Mäkipää who was elected Finns Party MP in 2011 and who hardly even speaks about immigration but rather about welfare issues and services in the rural ares. Furthermore, in the Kihniö council the local Finns Party group actually supported establishing a refugee accomodation centre in the municipality (even if they qualified it by saying that they wanted to choose what kind of refugees are coming).
If it were rural issues they might as well vote for the Centre Party, and if it were welfare there are two left-wing parties. The fact that individual politicians have shifted for one or another reason doesn't really prove that PS is different from SD. There was a prolific local Moderate politician who became an MP for SD because he felt SD had better Defense policy and didn't like the Moderates cuts to the military. A parliamentary candidate for the Christian Democrats switched because she felt SD was more anti-abortion. That doesn't mean that more than a handful people actually cast their votes for SD because the military, or that many people did so because of their view on abortion. Likewise the people who voted for PS because the Social Democrats or the Left Alliance are to Green must be neglectful at best.
There are people that vote for SD for all kinds of strange reasons, but 90% of those who do, have immigration and the EU as their reason. The same I'm certain is true for PS.