Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Stir in milk and sugar. Warm the mixture, stirring continuously, until sugar dissolves, 3 to 4 minutes. Turn Instant Pot® off. Add rice. Close and lock the lid.
Select high pressure according to manufacturer's instructions; set timer for 15 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, at least 10 minutes.
Beat eggs in a bowl. Remove lid of the Instant Pot®. Scoop 1 cup of pudding mixture out of the pot; add to the beaten eggs and whisk until completely blended. Pour back into the Instant Pot® and add raisins, vanilla extract, and cinnamon.
Select Saute function. Cook until mixture thickens, about 3 minutes. Serve warm or chilled.