Note the following, directly quoted from CMS (Chicago Manual of Style):
Definition and form
An
ellipsis—the omission of a word, phrase, line, paragraph, or more from a quoted passage—is indicated by ellipsis points (or dots), not by asterisks.
Ellipsis points are three spaced periods (. . .), sometimes preceded or followed by other punctuation. They must always appear together on the same line, but any preceding punctuation may appear at the end of the line above.
And the following from MLA (Modern Language Association):
The usual style of ellipsis is: space-period-space-period-space-period-space that is: Abed
e . . . hijklmn . . . tuww . . . (etc.)
Emphasis/italics mine.
The above example would therefore be rendered: "He disagreed . . . with my suggestion."
Also, the original query included quoted material, or, in this case what appeared to be dialogue. When material is already enclosed in quotation marks, those marks must be preserved in the re-quoting of said material. Thus: "Don't run so fast!" said the mother to her child
Would be re-quoted in a term paper (or whatever) as:
The text reads: "'Don't run so fast!' said the mother to her child."
Note also that I did say there were variations, however CMS is generally considered a bible of bibliographic usage, and is accepted worldwide. In the absence of specific requirements for a document being edited (such as the doctoral dissertation I just completed for a Université de Montréal student), CMS is the reference of choice.
Why UdeM is so lax in not having a specific guideline, I haven't a clue -- but it is a university with rather odd departmental quirks, and this is one of them.

This is not an area in which I merely dabble. I have 25 years of editing experience in several fields -- including language. Personally, one of the formats I detest is the MLA (Modern Language Association) method of citation, which to my eye looks sloppy overall. This said, both are consistent in stating that the periods in ellipses are preceded and followed by spacing.
This is why I pointed out that consulting the instructor for his/her preferences is the best route. I know professors in language who dislike MLA (the language standard for such things), and while they will accept it as standard, they prefer other formats. Using what is preferred will always get a higher standard of approval -- be that fair or unfair.
As an instructor in the language field, I was forced to use MLA for certain things. I always disliked it, and unless absolutely required, I will not use it, preferring instead CMS.