There are two ways to add or use a color in Adobe programs from Pantone Connect.

The "eye-dropper" icon will appear when hovering over a color in Pantone Connect. Clicking on the color while the eye-dropper icon is active will make this the active color in Adobe programs and if an object is selected in your design file this will change the color. Note that this will add this color as the active color in Adobe and will be based on the color settings of the Adobe file (RGB or CMYK).

Another method to add a color from Connect to Adobe is to add the color to the Swatches tool of Adobe. You can right-click on a color or when hovering over the color the menu icon (3 dots in upper right corner) will appear. Doing so will open the menu for this color with options of what can be achieved. You will see ADD TO SWATCH which will add this color directly to your Adobe file's Swatches tool as a 'spot' color (in L*a*b* color space).