you must add the excel sheet all over and preform the "join by attribute" again. the connection to excel is not dynamic. here is more about how to use Microsoft Excel files in ArcGIS:
When working with Microsoft Office Excel files, there are a few things to keep in mind:
ArcGIS supports both Excel 2003 and earlier.xls files and Excel 2007 .xlsx files. One advantage of Excel 2007 is that it allows much larger worksheets (1,048,576 rows by 16,384 columns) than you can have in Excel 2003 (65,536 rows by 256 columns).
If you have an .xlsx file you want to use in ArcGIS but do not have Excel 2007 installed, you will need to install the 2007 Office System Driver. It can be downloaded from the Microsoft Download Center. If you have Microsoft Excel 2010 or no version of Microsoft Excel installed, you must install the 2007 driver before you can use either .xls or .xlsx files.
Excel tables are read-only in ArcGIS as well as in Excel when you have a workbook open in ArcGIS.
Field names are derived from the first row in each column of the worksheet. You can view the properties, set aliases for the field names, and set field visibility on the Fields tab of the table's Properties dialog box.
Excel does not enforce field types for values during data entry like standard databases do. Therefore, the field type specified in Excel is not used in determining the field type exposed in ArcGIS.
Instead, field type in ArcGIS is determined by a scan of the values in the first eight rows for that field. If the scan finds mixed data types in a single field, that field will be returned as a string field, and the values will be converted to strings.
Best Answer
As mentioned in comments, I am not aware of any out-of-the-box way for ArcMap to symbolize layers using RGB values stored in an attribute table, or using RGB values in Excel joined onto an attribute table.
However, there is an existing ArcGIS Idea to Set symbol color from RGB values in attribute table so I recommend that you add your vote to that.
Note that the above ArcGIS Idea only covers:
So if you are wanting to do this for points, polylines or outlines of polygons then you may want to submit additional or more comprehensive ArcGIS Ideas.
Alternatively, if you use ArcGIS Pro, you can use a few lines of ArcPy/Python to calculate a hexadecimal color field from your RGB values and then use attribute driven symbology.
For more details see Using RGB values stored in field of feature class to apply colour component for ArcGIS Pro symbology?