Salaries gets higher too because of much corporate cash, there is this nasty infinite loop of inflation -> salaries -> inflation -> salaries.
This is why in the newspapers we occasionally see rants from the population that foreigners destroy the quality of life by pushing prices higher.
One cause is that there is a limited amount of space in Tallinn but high attractivity for IT foreigners (due to low taxes and high startup funding).
This means that good housing is though to find for a decent price (check kv.ee for example), and that there is not enough housing for everyone.
Not enough housing means lot of construction needed.
Lots of construction worldwide + scarce construction supply + abundance of money + lot of people = potential housing catastrophe.
Concretly, for example, I wanted to buy a reasonably priced house in the countryside (500K EUR for 160m2 / 1700sqft), and someone who sold his Pipedrive or Transferwise shares (I don't remember) came and offered over 100K more than the list price. This is very broken (and I say that though I am also a startup guy, so I feel it's sad/wrong for the non-IT Estonians).
The city also have 50K to 80K refugees that came in a few months. Where do you host them ?
Well, you pay high price for rent.