It's a mistake to think that Hitler was not on the radar of people living outside of Germany after (or even before) 1933. Remember, Germany was not only one of the largest countries in Europe by population and economy, but had also been a major participant in the recently-concluded First World War. What happened in terms of German domestic politics, therefore, was highly newsworthy in the 1930s. Nor was the nature of the Nazi regime a particular secret. It was very clear to international observers that Hitler was setting up a dictatorial, single-party state, based on the suppression of the left and the persecution of Germany's Jewish minority. While specific details may have been more obscure (such as the growing system of concentration camps), enough was an open part of Nazi rhetoric and policy that people in other countries had ample opportunity to develop strong opinions about Hitler, and for Hitler to become emblematic of dictatorship, though not yet of genocide.

Glaswegians would not have been alone in comparing disliked authority figures to Hitler in the 1930s. However, we can perhaps say a bit more about Glasgow as a specific context here. While it's possible to overstate the reality of Glasgow's reputation as a 'Red' city, there's no doubt that it was home to a particularly well-organised and politically active working class population, which had gained significant notoriety in the aftermath of the First World War (the famous 'Red Clydeside') due to a series of labour disputes, strikes and riots. This translated, across the interwar period, into Glasgow being home to unusually strong leftist political movements, including at various points the Communist Party of Great Britain, the Independent Labour Party and the Scottish Socialist Party, as well as the more mainstream Labour Party, all of whom were avowedly anti-fascist in one form or other. While forms of the extreme right did exist in Glasgow, they tended to follow existing sectarian tensions, with radical Protestant groups in particular making some gains in local politics, but without any real policies beyond the exclusion of (Irish) Catholics. Their political vision didn't really gel well with contemporary fascist movements, with the result that Glasgow - like much of the rest of Scotland for that matter - proved to be very unreceptive to the efforts of the British Union of Fascists in the 1930s. In other words, there was not really many people in Glasgow in the 1930s who was particularly inclined towards sympathy towards Hitler, and a great many who were actively politically opposed - depending on the district of Glasgow you are referring to, it might well have been a very logical point of reference just in political terms.

Even had it not been one of the parts of Glasgow like the Gorbals which was closely associated with far left politics, the usage would not have been that unusual. Off the top of my head, I can think of one quite interesting example of how far 'Hitler' had become shorthand for 'dictatorial' or otherwise anti-freedom. During the Spanish Civil War of 1936-9, there was a great deal of popular support in Glasgow for the left-wing Spanish Republican side, with these years seeing a quite remarkable and sustained solidarity campaign. However, some of the city's more well-heeled citizens, as well as some of the more devout Catholics, took a different view and supported Franco's rebels (who were backed by Mussolini and Hitler). In early 1938, they formed a branch of the nationwide organisation called 'Friends of Nationalist Spain', which attempted to counter the popular support received by the Republicans. This prompted a reaction on the part of pro-Republicans, and counter-protests at the meeting led to some violence. A second, larger meeting was planned at Glasgow's St Andrew's Hall, a public venue owned by the local council, which was then controlled by the Labour Party. After the Glasgow Chief Constable informed the council that he could not guarantee public order if the meeting went ahead due to the likelihood of large counter-demonstrations, the council decided to withdraw permission for the meeting.

This decision caused considerable turmoil in local politics - Labour nearly split over the issue, with several members (generally representing very Catholic wards) voting against, generally framing the issue as one of liberty and free speech. The local Catholic newspaper, the Glasgow Observer, adopted a similar line, with its headline on March 26, 1938 reading:

Corporation Hitlers Ban Franco Meeting – City Hall Let Revoked – Free Speech For Socialists Only?

This incident shows, I think, the extent to which the use of 'Hitler' had been normalised in Glaswegian public discourse by the late 1930s. Even a Catholic newspaper, which on this particular issue was on the same side as Hitler, used the term to bolster its attack on what it saw as the undemocratic actions of the city council. I don't doubt that you could find many more such uses in the 1930s, in Glasgow and elsewhere in Britain.