Hi Natalie,
An ArcGIS online Hosted Tile Layer is a Cached Map Service without a query ability, Essentially is just a picture. This functionality to query a raster is available for Image Service that are supported on ArcGIS Server Image Server extension The Configure pop-ups for imagery workflow here would then apply.
On this note, we don't have to step out of ArcGIS online to get the query going but it will take some more work.
we can Enable pop-ups on hosted tile layers. If we have Features to accompany the data, i.e. a Hosted Feature Service
Some of the additional work will be processing the Raster data into a Polygon so that it's lightweight for publishing as a Hosted Feature layer.
Having attributed Soil data may lend itself very well to the Raster to Polygon—Conversion toolbox | ArcGIS Desktop, I imagine If that output data is simple enough you might be able to publish it and utilize it in place of a tile layer altogether.