The rules require you to apply the wash sale rule across all accounts you own. The same would be true even if you held accounts at different fund companies or brokers.
Vanguard, on the other hand, is required to apply the wash sale rule on an account-by-account basis. You may have cross-account wash sales that are not flagged as wash sales in the reports you receive from Vanguard but are nevertheless required to be reported as wash sales on your tax return.
As a practical matter, unintentional wash sales that occur as a result of dividend reinvestment are unlikely to have more than a trivial effect on your tax liability, and unlikely to attract the attention of the IRS if unreported. To avoid any issue, though, you might consider eliminating automatic dividend reinvestment for your holding in this mutual fund. You can manually reinvest the dividends from time to time, avoiding purchases during periods when they would trigger wash sales.