Did they inject the vaccine before the finished the trials?Depends what you mean.
The basic pre-trial scientific development time is comparable to other vaccines, and it is entering more extensive trials in a time frame similar to other vaccines. This would suggest that notionally, at a scientific level it is following a development course similar to others. That said, there are significant concerns. Firstly, a lack of transparency in supporting information about its development, and suggestions of ethical breaches in the safety trials. Either might lead to rejected approval in many countries.
If we mean approval, Russia has most definitely rushed approval for use (in Russia) as it plainly had not completed (or even started) the trials normally demanded. I don't see other countries ready to approve it for that reason, or much evidence of it being rolled out in Russia despite approval. That (and the name) is why I think the approval was a PR stunt by the Russian government: they wanted to put up Russia to the world as a country that could keep pace with the West, Japan, China, etc. If the vaccine ends up effective and well used, great. If not, oh well. But they got their headlines even if the latter is true.
I heard there are some 30 countries lining up to Russia for their vaccine. It is very likely this is a PR move. I think they want to avoid quarantine despite the virus, Russia was in lockdown for an extended period of time