The problem is that "tutorial" does not really address setting up spot colors in Photoshop. In fact, it's completely inaccurate for production.
You can't simply pick a spot color and use it on a layer. It's not that simple. That's not how Photoshop works with Spot colors.
The writer of that article should be flogged with a wet noodle repeatedly. Anyone savvy enough to want to use spot colors, most likely wants them to reproduce properly, otherwise there's no point to using spot colors.
In order for InDesign to see and recognize spot colors in a Photoshop file, you need to configure Spot Color Channels within Photoshop. This means you have to create new channels for each of your desired spot colors and then alter the pixels on that channel for areas you want that color to appear.
When working with spot colors in Photoshop, all the editing is on the channels and not in layers.
Try this article first: http://planetphotoshop.com/working-with-spot-color-channels.html It's a decent explanation of Spot color channel set up.
This is also decent http://layersmagazine.com/spot-color-separations-in-photoshop-cs5.html --- However, you can ignore the last step regarding saving as DCS, just save as a .psd for InDesign. (Note for QuarkXPRess, you do need the DCS2 format. PSD won't work for XPress, but works fine with InDesign.)
Here is another decent run down: https://www.rockymountaintraining.com/adobe-photoshop-working-with-spot-color-channels/