But if people democratically control the socialist government then one could argue it is still a democratic socialist government. As opposed to say a dictator running a socialist government.
Democratic control of a socialist country can never happen.
In a land of millions, you can't govern by the popular will of the majority vote. The majority is uneducated, uninformed, easily lured and uninterested in politics. The usual form of democracy winds up like ours: a representative government. You vote for the reps, and they vote on the issues.
Even if we had a voting population interested enough and informed enough to intelligently vote on every single issue, the logistics of holding election after election would be cost and time prohibitive. In this case, you'd also run into Tyranny of the Majority, where the majority always wins, and the minority has no voice in any issues. Depending on the majority to pass laws that benefit the minority is not going to turn out fairly, Case in point: Gay Marriage. Many states held elections, and the majority voted against legalizing Gay Marriage. Those votes were overturned by federal mandate
Those elected to represent you will find ways to leverage that power for their own profit. They will do so in the name of equality and the good of the state. That will end "democracy".
Power corrupts ...
Ask yourself WHY no examples of Democratic Socialism exist in the world ... ever.