How is the choice made by Nicholas II between "также" and "так же" in his Language Manifesto of 1900 correct?

Since on the source site you gave a link to there is a typo or an OCR mistake in the word установяенія instead of the correct установленія, I decided to check the original printed version of the manifesto if также is also a digitizing mistake. I found it in a scan of "Полное собраніе законовъ Россійской Имперіи" and it is really также there (scan pages).

Также in that manifesto is definitely a mistake, and we'll never know at which stage it appeared. Также and так же were well differentiated already in the beginning of the 19th century. In his monumental Explanatory Dictionary of the Live Great Russian Language (1863–1866), Vladimir Ivanovich Dal (Dahl) wrote, volume 4, page 354, entry for the word "такъ":

Такъ же, такимъ же образомъ, способомъ, порядкомъ, одинаково. Задача эта рѣшается такъ же, какъ та. Пишутъ и также, и это правильно, гдѣ означаетъ: то жъ, то же, (нѣмцк. auch.) И я также пойду, также хочу, и мы также были тамъ.

Anyhow, it was a mistake to have также in that sentence of the manifesto, let's blame the corrector who should have noticed it when preparing the document to be officially printed.

And finally, have a look at this Google Ngram chart. As you can see, during the last 220 years the relative frequency of также and так[ъ] же has not changed which means in the times of Nicolas II the rules for the choice of these two words were the same as now: