When a workbook that is not checked out is opened in Excel 2016 using DMS it is opened in read-only mode regardless of the Auto check-out Excel workbooks on open setting.
This is because the default behaviour when opening Excel files from SharePoint using Excel 2016 has been changed by Microsoft (see below blog for more information):
Microsoft’s rationale for this change appears to be to ensure that Excel documents are not opened from SharePoint in edit mode without the user consciously selecting ‘Edit Workbook’ in order prevent locking out other users from editing the file. MacroView's philosophy with regard to DMS functionality is to enhance the experience when working with SharePoint while respecting standard Microsoft functionality and as such does not change this default behaviour.
The impact of this is that Excel documents opened in Excel 2016 via MacroView DMS will always open in read-only mode unless both auto checkout is enabled (i.e. Auto check-out Excel workbooks on open setting is checked) and Open documents read-only by default is disabled, or if Auto check-out Excel workbooks on open is un-checked and the document has already been checked out to the current user.
If you want Excel documents opened via MacroView DMS to be checked out by default we recommend the Auto check-out Excel workbooks on open setting is checked and you make use of the right-click Check Out option before opening Excel documents for editing (as is currently required for all document types in the browser).
If you do not want Excel documents opened via MacroView DMS to be checked out by default then uncheck Auto check-out Excel workbooks on open under DMS Options, then after opening the document, select Edit Workbook if editing is required.
Note: When using MacroView Enhanced Versioning/Auto Numbering, Auto check-out Excel workbooks on open must be checked.