While I can't speak for every democratic socialist movement in history I can provide an answer from the perspective of the swedish Social Democratic Party (Socialdemokraterna).

Social Democrats or Democratic Socialists

While the swedish Social Democratic Party's ties to democratic socialism an an ideology are not as strong today as they once were (as the party has increasingly moved toward the centre of the political spectrum in recent years), democratic socialism was the core principle of the party for the majority of the party's existence. And although the principles of democratic socialism are not as explicit in the party's rhetoric as in the past it is still part of the party's identity, for instance appearing as a section in the party programme of 2013. Link to the party programme PDF. The section is on page 4.

Having established that the Social Democrats were (and to some extent still are) democratic socialists let's examine your question; did they openly criticize communist regimes? To answer I will give three examples of Social Democratic policy and rhetoric that was anti-communist in nature. Bear in mind that all examples are criticisms presented against the Soviet Union and Eastern Bloc. I am fairly certain there exist criticism of Mao's China as well, though I don't know it as well and don't have any sources at hand.

Ådalen 1931

The first example is not necessarily criticism against communist regimes, but helps demonstrate the split between democratic socialists and communists. It revolves around the aftermath of the 1931 Ådalen shootings, where 5 people were shot dead by military personell during a workers' demonstration against strikebreakers. The shooting caused massive ripples throughout swedish society and all political parties immediately scrambled to offer their respective responses to the crisis. These responses were primarily published through party-affiliated newspapers.

Right-wing papers responded by saying that the shootings were caused by armed communist agitators from Moscow inciting the crowds to violence, and that there was need for a crackdown against socialists. Communist papers on the other hand claimed the military was solely responsible for gunning down the peaceful protesters, and that the shots would signal the start of the true class war. Social democratic papers took up a left-leaning perspective of the shootings, but one that differed from the communists'. According to the Social democratic papers the military was primarily to blame for the shootings, but rather than class war the shootings were a tragedy that needed to be resolved peacefully rather than through violent revolution. They attributed the cause of the shooting to the inequality and lack of workers' rights in Sweden at the time, and urged for reform to prevent similiar events in the future. The reasons for the social democrats pushing a different narrative from the communist are many, but much of it boils down to wanting to prevent the Soviet-friendly communists from gaining ground as the social democrats did not view the Soviet Union as a model to be followed.

This infuriated the communists who viewed the Social Democratic version of events as a betrayal of the victims and the labour movement as a whole. While there had been splits between the communists and social democrats before, this disagreement furthered the rift and would not be reconciled until the right-wing victory in the general elections of 1976.

The National Unity Government

The second example takes place during WWII, where the parties of the swedish parliament decided to form a National Unity Government under the leadership of the social democrats (as they were the largest party). The purpose of the NUG was to ensure stability during the wartime years and prevent Sweden from being dragged into the war. However, due to the aggressive foreign policy of the Soviet Union the pro-soviet communist party was excluded from the NUG. Many of the NUG's policies during the war focused on not giving Germany any reason to take military actions against Sweden as it had done with Denmark and Norway, which provided part of the reason for why the communists were excluded.

Another reason for the exclusion was the Soviet Union's invasion of Finland, which turned the majority of the Swedish population (including the social democrats) against the communists as many saw the Finns as a "brother people". While the Swedish government did not offer official military support to Finland, it did allow and help organize significant volunteer forces to assist in the finnish war effort. The government also attempted to initiate peace talks between the warring parties, and when the Soviets finally agreed to negotiate with the Finnish government social democratic prime minister and leader of the NUG Per Albin Hansson wrote in his diary that it was a great success.

To recap this part, during World War II the social democrats intentionally excluded the communists from participating in the national government, and adopted as much of an anti-soviet stance as they could without risking war with either Germany or the USSR. It should also be mentioned that during the wartime years several Swedish communists were arrested and confined to labour camps, as their connections to the Soviet Union were viewed as a threat to national security.

Olof Palme's Speech

Now the most fitting example of a democratic socialist critizing authoritarian communist regimes comes from one of the most renowned Social Democrats in swedish history; Olof Palme. Palme was appointed leader of the party in 1969, and served as Prime Minister during the years 1969 - 1976, as well as from 1982 until he was murdered in 1986. During the campaign for the general election in 1982 Palme appeared on a debate with the other parties' leaders on national television. At the end of the debate Palme performed as speech called "Why I am a Democratic Socialist", where he sought to underline the values that signified his political position. He begins the speech with the following segment, where he explains why he became a democratic socialist specifically (my translation):

I am a democratic socialist, with pride and with joy. I became one when I traveled throughout India and saw terrible poverty while some were incredibly rich. When I traveled and saw an, in some ways, even more humiliating poverty in the United States. When I, as a young man, came face to face with communism's lack of freedom and oppression, and the persecution in the communist states. When I came to the nazi concentration camps and saw the lists of dead social democrats and trade unionists.

[The whole speech can be watched here with english subtitles, though some are a bit paraphrased.] (https://www.youtube.com/watch?v=7i2Ws1X5DSA)

Summary

From a Swedish perspective communism and communist states, primarily the Soviet Union, have a long history of being distinctly split from and criticized by the democratic socialists represented by the social democratic party, which ruled the country for most of the 20th century and created the Nordic Model that Bernie Sanders (and others) have held up as inspiration for his suggested policies.