Due to Excel's internal floating point numbering scheme, it appears that there is a known 15-digit limitation:
(Note that Tableau seems to have the same 15-digit floating point constraint for measurements and mathematical calculations.)
I recreated your scenario, and it still exports to Excel in scientific notation even when the Acquirer Reference Number is in Tableau as a Dimension and even when it is also transformed to a "String" type.
The only workaround I've found is to use the "Export Crosstab to Excel" option instead of "Exporting Data" as shown below in the "Worksheet" Menu. The outcome is comparable to adding an apostrophe before each cell in the Excel workbook. It lacks beauty and has restrictions, but it might help you achieve your goals.