From a Liverpool perspective I would be very upset by the reaction in Uruguay. They did well to manage his return and I assume it has something to do with the sports psychologist that works with them (Peters?). Yet as soon as he is away with Uruguay he reverts to type. The heroes welcome in Montevideo will only reinforce his view that he is did nothing wrong and is persecuted.
And if I was at Liverpool I would be thinking just like galeforce described, just hoping the Uruguay team, management and president would shut-up and stop making things worse.
i doubt they did any "work" with him. they definitely did not tell him to stop diving/cheating. i suspect someone just had a quick word with him about trying to think about his conduct on the pitch a bit more. that will have been the extent of the "work" that liverpool would have done with him imo.