When you set DeepL to translate the selected text, the DeepL website opens in a new window the first time you translate the selected text, if you keep the window open the next texts will be translated without changing tabs.
And in the extension settings there is an option to translate the selected text by pressing Ctrl twice, if you press Ctrl only once and this window is opening your keyboard may have a double click or something unusual is happening.
Please create an issue on GitHub: https://github.com/FilipePS/Traduzir-paginas-web/issues/new