Although I am a Benefits Director, I obviously don't manage your plan. I do have to agree with you that it would be a best practice to clarify the timing of the employer deposit to avoid participant confusion. In my plan document, we have it worded as "the Company's contribution will be made within 30 days following the end of the contribution period." Our contribution period is further defined as ending on December 31. So we have until January 30 to make this deposit. Our Plan year can still be defined as January 1 to December 31.
The way your plan is worded (if that is it's entirety) does not make it clear and thus your confusion about why it isn't deposited by the 31st. However, it is permissable by ERISA and the IRS to make the employer contribution count towards the prior year (including the combined contribution limit) as long as it's done with 30 days of the due date of the company's tax return. For most companies this is October if they file for an extension every year.
It would be rare indeed that a company match was so generous as to go over the combined contribution limits. In 2019, the limit is $56,000. Assuming you put in $19,000 of your own money the company match or profit sharing contribution would need to exceed $37,000 to be of issue. If you are over age 50, there is of course the additional $6,000 in catchup contributions allowed.
I'm not sure if you've received a response from your company yet, but I think you are suggesting that they clarify the timing of the deposit to set employee's expectations correctly and also whether there is a requirement to be actively employed either on the last day of the Plan Year or the date the deposit is actually made. Hopefully, they will see the value in addressing both of your concerns. You mentioned the company is 45 people, so this sounds like it probably is a 'small retirement plan' (not subject to external annual audits). These are both concerns an external auditor may have suggested the sponsor make to tighten up the documentation and thus compliance.