The article you listed talks about Krugman, Obama, and such neoliberal centrists. There was no "progressive Berniecrat" wing of the Democratic party at the time (I mean among the ranks of the party, not in the hearts of voters). So if anything it shows that the neoliberal Democratic party when Obama ran for office was hostile to immigration (more openly hostile than anything Bernie said).

Bernie and a few other Democrats opposing the 2007 immigration bill on that very argument.

They opposed it for many reasons, including the fact that it was a double edged sword: the type of visas it would give guest workers would make them ripe for exploitation. That's explained in their policy platform on immigration. A similar bill in 2013 that addressed some of the issues about exploiting guest workers was supported by Bernie (the change of mind indicating the difference was more about the treatment of guest workers than about suppressing of domestic wages, though Bernie admittedly also talks about the latter a lot). In their policy platform they talk about how that isn't enough and how they would support reforming it so that guest workers are treated with the same type of workers rights as domestic workers. They also want to give citizenship to 11 million non-citizens already in the US (legal or not). I fail to see how this is against immigration, let alone more restrictive than Hillary's or Obama's position.

That being said, I think a lot of Democrats/progressives/socialists/etc. have become much more liberal on immigration, something I'm quite happy about btw.

Socialists (the libertarian ones at least) want no states, no borders, no countries.

Progressives like Bernie are typically misunderstood when talking against trade agreements or workers rights (like that 2007 bill).

Democrats have probably become more liberal when it comes to immigration, though Obama deported more people than any other president before him.