Allen was waiting in the workshop with his blade beside him.
Professor Adrian promised to engrave runes on his blade. He had the funds to ask for a professional and more experienced Runesmith to tune his blade. However, he has experienced the talent of that man whom the world deemed a failure.
When Allen first heard 'her' voice and the praises she sang about Adrian, Allen wasn't able to trust her. That's why Allen even volunteered to be the test subject of the Professor during the assessment. He wanted to see if 'her' words actually held any weight.
And also, the reason why Allen got interested in Olivia to begin with was because of Adrian.
...well, it was another thing that slight curiosity turned deeper and now they share a relationship. He doesn't regret it, as he told Olivia, but yes, it was unfair to Adrian.