There are situations when something being contrastive doesn't necessarily mean intentional implication. Contrast lays in possibility of several candidates, especially so binary pairs like speaker/listener, while implication lays in our intention to deliver information indirectly. And while it's impossible to imply without having several options, having several options doesn't have to bring implication.
Some of such examples can be 実は or 今日は. Both have a very strong contrast with a lie and other days, but at the same time both are often used without intention to imply anything else. The main factor in figuring out whether person tries to imply something or not, in my opinion, is mutual understanding. The more and better people know each other, the easier to deliver intended meaning indirectly using wording, gestures, facial expressions and other things. Culture also affects it, for example, generally Japanese people try to praise others and humble their own achievements, and such things like insults would go against it. This leads to a situation that people's faults often would be expressed indirectly, and it changes people's understanding. All situations related to praises have higher chance to include implication, people become conscious of it and either start to use or avoid it.
My opinion about は differs in some places from classical は explanations. I look at it from more practical view, and in my opinion は strongly relates with our feeling about what we want to talk. Such way if person wants to talk about 父 and still keep it within 休みの日 context, there is no other way than to mark both by は particle. Comparing to other double-triple subject sentences like 象は鼻が長い, that can be transformed into 象の鼻は長い and other variations, 父は休みの日はずっとテレビを見ている is much more rigid. Despite both contrast and implication are connected, if we want to talk about implications, we have to look not to much at contrast, but speaker's intention.