No need to worry too much! While any produce should ideally be refrigerated as soon as the box arrives, nothing else tends to be perishable, and luckily the state of any produce is rather easy to tell. Products of nature can sometimes behave unpredictably, so please use your best judgment. If the produce seems okay to you, then feel free to use it! But if it looks like anything has begun to turn, it may be better to purchase replacements.
Our house-made syrups are shelf stable and need to be refrigerated only once they've been opened, so they'll be just fine. Bitters could begin to evaporate over time if left out in high heat, but everything else should be a-okay :)