He was quite obviously a suspect, in fact the only suspect, from the moment the cops arrived on the scene. Indeed, almost certainly before that. It's absolutely astonishing how early they jumped to the conclusion that he did it. Regardless of what Craig Dobbie says.
It's an interesting parallel with David Gilroy. I think it's likely they hadn't seriously considered him as a suspect up to the point of the phone call at Lochgilphead. But even then they were probably aware that his behaviour was a bit odd. After it took him a couple of hours longer to get back from Lochgilphead than it should, though, cogs were definitely turning.
By the time he was being questioned in the police station at Corstorphine he was absolutely definitely a suspect, he had to be, but they still persisted in declaring that he was only a witness to justify not cautioning him and not giving him the opportunity to get a solicitor. I think that was the basis of his appeal.