The English expression "working hours" normally refers to fixed times during the day, such as "9:00–17:00", but the Italian expression "impegno orario" seems to always refer to the total _number_ of hours one is required to work for one's employer, e.g., "40 hours/week".

So, the document does not seem to be specifying any particular time of day when the experiment is to be carried out (e.g., "after 6 P.M.", "after hours", "after work") but instead seems to be saying that the hours that employees spend on the experiment _will not be counted toward_ the hours that they are required to work for Azienda Ospedaliera Papardo (AOP).

Hence, under "l'obbligo di timbratura da parte del personale", an employee might, during the hours that he/she normally is at work there, "clock out" for half an hour to work on the experiment and then "clock in" again to continue on regular hospital work, all of this during his/her or the hospital's "[normal] working hours".

As a result, in spite of the wording "svolta fuori", I believe that the best way to translate into English the phrase "l’attività di sperimentazione deve essere svolta fuori dall’impegno orario istituzionale" would be something along the lines of "the hours spent on activity related to the experiment must not be counted toward the number of hours that employees are required to work for AOP."