Improving user engagement and platform revenue is crucial for online marketing platforms. Uplift modeling is proposed to solve this problem, which applies different treatments (e.g., discounts, bonus) to satisfy corresponding users. Despite progress in this field, limitations persist. Firstly, most of them focus on scenarios where only user features exist. However, in real-world scenarios, there are rich contexts available in the online platform (e.g., short videos, news), and the uplift model needs to infer an incentive for each user on the specific item, which is called real-time marketing. Thus, only considering the user features will lead to biased prediction of the responses, which may cause the cumulative error for uplift prediction. Moreover, due to the large-scale contexts, directly concatenating the context features with the user features will cause a severe distribution shift in the treatment and control groups. Secondly, capturing the interaction relationship between the user features and context features can better predict the user response. To solve the above limitations, we propose a novel model-agnostic Robust Uplift Modeling with Large-Scale Contexts (UMLC) framework for Real-time Marketing. Our UMLC includes two customized modules. 1) A response-guided context grouping module for extracting context features information and condensing value space through clusters. 2) A feature interaction module for obtaining better uplift prediction. Specifically, this module contains two parts: a user-context interaction component for better modeling the response; a treatment-feature interaction component for discovering the treatment assignment sensitive feature of each instance to better predict the uplift. Moreover, we conduct extensive experiments on a synthetic dataset and a real-world product dataset to verify the effectiveness and compatibility of our UMLC.