Gerry, by his own estimation, pinpointed Kate's alarm around 10.13pm.
"Half and hour later without anything to signal, it being 22h03, he turned to alert KATE that it was time for her to go to see the children. She immediately made her way to the apartment by the usual path, she having entered by the rear door. About 10 minutes later, he started to worry about her lateness and, at the moment he prepared to stand and to go to see the reason for her lateness, KATE appeared running, completely distraught and crying, saying that MADELEINE had disappeared and that she was sure because she had looked throughout the house."
Add to this the eyewitness account of Svetlana Vitorino....
"
------- STARIKOVA VITORINO (Russian citizen, with the telephone No "96635 ####) - kitchen assistant:
- Said that, yesterday, one individual, purportedly the father of the missing, left the dinner table where a group of friends (in number 8 or 9), for about 30 minutes. After having returned, a woman whom she believed to be his wife, also left the table, there having passed a few moments, all the guests left the table in question, except one elderly lady, who told her [Svetlana's] colleagues that that child had disappeared.
And an argument can certainly be made for the first scenario you suggest ie an alert around 10.15.