Using product tie-ins when creating promotional umbrellas is a good way to kill two birds with one stone and you can also split the manufacturing costs with another company should you decide to do a product tie in with a different company. Basically using a product tie it with your promotional umbrella can go one of two ways.
Should you wish to promote your own product, as well as your company's name, you would create a promotional umbrella that advertises not only your product but also your company's logo slogan or name. This is easy enough to do as you will have control over both the marketing of your product as well as the marketing of your corporate logo. That is to say when designing a promotional umbrella you will have complete control over the color scheme used in both your company's logo as well as your products logo. This allows you to create a unified looking promotional umbrella that will not look sloppy but rather will look put together and well-designed.
This is of course advantageous over a promotional umbrella that is designed by two different companies and may not have the same unified visual appeal. You will however want to differentiate between the two logos on the same promotional umbrella even if you are creating both of them. The reason for this is simple. Although your company has created a product that you are advertising, the company itself should still be advertised as a separate entity because it is more then just the one product. In the long run this separation of product advertisements from company advertisements, whether on a promotional umbrella or in general, is a good idea for any company to follow.
An additional level of complexity is added to the equation when two different companies have a stake in designing the same promotional umbrellas. Naturally the two disparate companies are going to have different ideas for how they want their product marketed, be it in design or color choice. Well it can be daunting to design a promotional umbrella that meets the needs of both companies it does not necessarily have to be that difficult. In fact you can actually use less design on the promotional umbrella when doing a design for two different companies than you would if you are only designing for one company.
Think of it this way; when you are designing for two different companies on the same promotional umbrella you can use somewhat of a mosaic technique to incorporate both companies products, logos, graphics or whatever. People will be expecting a somewhat disparate look, so even if your promotional umbrella does end up looking a little bit pieced together it will still be deemed as visually acceptable to most people.
If you do want to design to look for your promotional umbrella and you are dealing with two different companies communication is the key. It is only through ample communication that the two companies will be able to get together and design a promotional umbrella using a unified color set and visual theme.