The oblique infinitive followed by के साथ ही indicates an immediate consequence and can be translated “as soon as …”.
Consider a few examples:
उपग्रह वातावरण में प्रवेश करने के साथ ही जलने लग गया – “As soon as the satellite entered the atmosphere, it began to incinerate”
कंपनी की यह घोषणा करने के साथ ही, स्टॉक की कीमत घट गयी – “As soon as the company made this announcement, its stock price decreased”
Note that this idiom can be used without के (e.g. करने साथ ही), but it is perhaps more proper to include the full postposition.