They were using the universal calendar. It's just that the universal calendar periodically goes through upgrades, and not everyone adopts the upgrades at the same time.

The upgrade that the Russians were slow in adopting was the Gregorian calendar reform of 1582, which modified the previous Julian Calendar. Although the Russians were laggards, two things should be noted. (1) Eastern Europe as a whole largely stayed on the Julian Calendar until the early 20th Century. And (2) the English-speaking world didn't switch over to the Gregorian system until 1752, so it's not like we were particularly snappy about it either.

The reasons why the English world and Eastern Europe were resistant to the Gregorian calendar reform were similar: religion. One of the main issues underlying calendar reform was the celebration of Easter, which has a complicated formula, and which the Church was concerned about getting wrong due to calendar drift. The Catholic Church addressed this with the Gregorian reform (so named because it was instituted by Pope Gregory XIII), but Protestants were suspicious, and it took them longer to get on board.

Eastern Orthodox churches were even more reticent, and the ecclesiastic calendars in many Eastern European countries still have not made the change to this day, even though the day-to-day civic calendars have. (This is why you will find that Christmas is celebrated in early January, by the Gregorian calendar, in many of those Eastern traditions.)

You actually have it backwards: the "universal calendar" is the Gregorian Calendar, and it was an update to the calendar that was used in Russia prior to 1918, ie, the Julian Calendar.

The Gregorian Calendar was introduced in 1582, and as it was a reform backed by Pope Gregory (hence the name), European Catholic states adopted it right away. The issue that it was correcting was that a discrepancy had arisen between the astronomically-observed year and the calendar year of 365.25 days: a drift of some 3 days every 400 years had crept into the calendar, and the Pope resolved to eliminate the drift by cutting 10 days from the calendar (and also changing the number of leap years in a 400 year cycle) so October 4, 1582 was followed by October 15, 1582

Protestant states were much slower to adopt the new calendar, with the switch coming in the 18th century (this is why, for instance, one sometimes sees Washington's birthday as Feb 22 (Feb 11 Old Style) 1732, as Britain and its possessions didn't switch to the Gregorian calendar until 1752.

Among Orthodox countries, Russia was not unique in being on the Julian Calendar, and all switched to the Gregorian during World War I and its aftermath: Bulgaria in 1916, Russia in 1918 (Jan 31, 1918 was followed by Feb 14, 1918), Serbia and Romania in 1919, and Greece in 1923.

So the issue was less that Russia was using a "different" calendar, but that, like other Orthodox countries, it was slow to adopt a new calendar originating from the Catholic Church, and only finally adopted it when it had wide acceptamce across Europe, and was seen as the "modern" calendar, especially by the revolutionary Bolshevik government in 1918.