On the last line of that log file you can see there's been 128 warnings, that's quite a lot. Can you filter those out (there's a button at the top of the log window for that) and see what they say? It should be a pretty good indication of what's going on here.

Thank you very much. I had seen the warnings but many times FME imported the data even if I had warnings. Now it seems that there were some columns in the excel that contained text instead of integer and because of this no import was done but at the end it showed me that the data was imported.

Thank you very much for your support

In this case it's FME handing the data over to the database and then the database not actually writing it because of the wrong data type. This does generate a warning in the FME log but it doesn't stop the process. As far as FME is concerned, as soon as it passes the data to Postgres it's done, so that's why you get the message saying translation succesful.

As a general rule of thumb, when you get warnings in your log you should always check them out.